Is the function f (x) = sin x even, odd or neither? | Socratic
2015年10月31日 · Odd By definition, a function f is even if f(-x)=f(x). A function f is odd if f(-x)=-f(x) Since sin(-x)=-sinx, it implies that sinx is an odd function. That is why for example a half range Fourier sine series is said to be odd as well since it is an infinite sum of odd functions.
Is the function y=x-sin(x) even, odd or neither? - Socratic
2016年7月20日 · The function will be odd. For an even function, f(-x) = f(x). For an odd function, f(-x) = -f(x) So we can test this by plugging in x = -x: -x - sin(x) = -x + sin(x) = (-1)(x - sin(x)) This means the function must be odd. It's not surprising either, since x and sin(x) are both odd. In fact, given two functions, f(x) and g(x) for which: f(-x) = -f(x) g(-x) = -g(x) It is obvious that: f(-x) + g ...
Is sine, cosine, tangent functions odd or even? | Socratic
2015年2月28日 · y = cos x is always going to be even, because cosine is an even function. For example, cos #pi/4# in the first quadrant is a positive number and cos #-pi/4# (same as cos #pi/4#) in the fourth quadrant is also positive, because cosine is positive in quadrants 1 and 4, so that makes it an even function.
How do you determine if F(x)=x^3-x is an even or odd function ...
2016年3月23日 · F(x)=x^3-x is an odd function. A function is even if F(–x)=F(x) and a function is odd, if F(–x)=-F(x). As we have F(x)=x^3-x and F(-x)=(-x)^3-(-x)=-x^3+x = -(x^3 ...
How do you determine if f(x)= e^x is an even or odd function
2016年3月15日 · Iff(-x) = f(x), f(x) is an even function of x.. If f(-x)=-f(x), f(x) is odd. Otherwise neither, like e^x.. e^x>0 and e^(-x) is the reciprocal 1/e^x.
How do you determine if f(x) = x+1 is an even or odd function ...
2016年3月31日 · neither >To determine if a function is even/odd the following applies. • If f(x) = f( -x) then function is even ,AAx Even functions have symmetry about the y-axis. • If f( -x) = - f(x) then function is odd , AAx Odd functions have symmetry about the origin. Test for even : f( - x) = (-x) + 1 = -x + 1 ≠ f(x) , hence function is not even Test for odd : - f(x) = -(x + 1) = -x - 1 ≠ f( -x ...
Is the function f(x) = x^3 + x sin^2 x even, odd or neither? - Socratic
2015年8月16日 · A function is even if if exhibits the property #f(-x) = f(x)# A function is odd if it exhibits the property #f(-x) = -f(x)# Let check for #f(x)#: #f(-x)# #= (-x)^3 + (-x) sin^2 (-x)# #=-x^3-xsin^2 x# #=-f(x)# Thus, #f(x)# is odd. You can confirm this by graphing. Since #x^3# is odd and #xsin^2 x# is odd, therefore #f(x)=x^3 + xsin^2 x# is odd.
How do you determine if F(x) = x + 3 is an even or odd function ...
2016年9月5日 · neither even nor odd. To determine if F(x) is even/odd consider the following. • If F(x) = F( -x) , then F(x) is even Even functions have symmetry about the y-axis. • If F( -x) = - F(x) , then F(x) is odd Odd functions have half-turn symmetry about the origin. Test for even F( -x) = (-x) + 3 = -x + 3 ≠ F(x) Since F(x) ≠ F( -x) , then F(x) is not even Test for odd -F(x)=-(x+3)=-x-3≠F ...
How do you determine if f(x)= sin x is an even or odd function ...
2016年3月23日 · To determine if a function is even / odd the following applies. • If a function is even then f(x) = (f(-x) , for all x. Even functions have symmetry about the y-axis. • If a function is odd then f(-x) = - f(x) , for all x. Odd functions have symmetry about the origin. Test for even : f(-x) = sin(-x) = -sinx ≠ f(x) → not even. Test for odd :
How do you determine if #f(x)= x^3 + 1# is an even or odd
2016年5月17日 · neither >To determine if a function is even/odd consider the following. • If f(x) = f( -x) , then f(x) is even Even functions have symmetry about the y-axis. • If f( -x) = - f(x) , then f(x) is odd Odd functions have symmetry about the origin. Test for even f(-x)=(-x)^3+1=-x^3+1 ≠f(x) Since f(x) ≠ f( -x) , then f(x) is not even. Test for odd -f(x)=-(x^3+1)=-x^3-1≠f(-x) Since f( -x ...