Let f(x) =2x+1 and g(x)=x^2-1. Find the following

Question

(gof)(2x)

Answer 1

The functions are f(x) = 2x + 1 and g(x) = x² - 1

f(x) = 2x + 1

f(2x) = 2(2x) + 1

f(2x) = 4x + 1

 

(gof)(2x) = g(f(2x))

= g(4x + 1)

Now substitute this expression (4x + 1) in to function g in place of the x value.

= (4x + 1)² - 1

= (4x)² + (1)² + 2(4x)(1) - 1

= 16x² + 1 + 8x - 1

(gof)(2x) = 16x² + 8x.