Let f(x)=4x^2+x+1 and g(x)=x^2-2. Find g(f(x)).

Question

Show each step for solving the question

Answer 1

g(f(x)) means that you will take the equation f(x) and substitute it for x in the equation g(x).

 

For example:

 

if f(x) = 2x + 3 and g(x) = x^2,

then g(f(x)) = g(2x+3) [substitute the equation f(x) for x]

 

since g(x) = x^2

then g(2x+3) = (2x+3)^2

so g(f(x)) = (2x+3)^2 [You will still need to expand and solve the equation.]

 

Answer 2

g(f(x) = (f(x))² - 2

g(f(x) = (4x² + x + 1)² - 2

g(f(x) = 16x⁴ + 8x³ + 9x² + 2x + 1 - 2

g(f(x) = 16x⁴ + 8x³ + 9x² + 2x - 1