Question

Let g(x) = cos(x/2) - 3x. Let f(x) = 2x + 5. What is g(f(x))?​

Answer 1

Answer:  The required value of g(f(x)) is $\cos\left(x+\dfrac{5}{2}\right).$

Step-by-step explanation:  We are given the following two functions :

$f(x)=2x+5,~~~~~g(x)=\cos\left(\dfrac{x}{2}\right).$

We are to find the expression for g(f(x)).

To evaluate g(f(x)), we need to find g of the function f(x).

We have

$g(f(x))\\\\=g(2x+5)\\\\\\=\cos\left(\dfrac{2x+5}{2}\right)\\\\\\=\cos\left(x+\dfrac{5}{2}\right).$

Thus, the required value of g(f(x)) is $\cos\left(x+\dfrac{5}{2}\right).$

Answer 2

Answer:

cos(x + $\frac{5}{2}$) - 6x-15

Step-by-step explanation:

Given g(x) = cos($\frac{x}{2}$)-3x

g(f(x)) = cos(f(x)/2) - 3(f(x)) where f(x)  = 2x + 5

        = cos((2x+5)/2) - 3(2x+5)

        = cos(x + $\frac{5}{2}$) - 6x-15