Question

Given the definitions of f(x) and g(x) below, find the value of (fog)(-3).

f(x) = -4x + 7
g(x) = 2x2 + 5x – 8

Answer 1

To find the value of the composite function (fog)(-3), calculate g(-3) which is -5, then plug this into f(x) to obtain f(-5), which results in a final value of 27.

Step-by-step explanation:

The composite function (f ∘ g)(x), also known as the composition of f and g, is found by substituting g(x) into f(x). To find the value of (f ∘ g)(-3), you first evaluate g at -3, then take the result and plug it into f.

• Calculate g(-3): g(x) = 2x2 + 5x - 8
  
  g(-3) = 2(-3)2 + 5(-3) - 8 = 18 - 15 - 8 = -5.
• Find f(g(-3)): f(x) = -4x + 7
  
  f(-5) = -4(-5) + 7 = 20 + 7 = 27.

Therefore, the value of (f ∘ g)(-3) is 27.

Answer 2

-93

Step-by-step explanation:

Step one:

given the expressions

`f(x) = -4x + 7\\\\g(x) = 2x^2 + 5x- 8`

we want (fog)(-3).

but (fog) is

`f(x) = -4x + 7\\\\\ (fog)=-4(2x^2 + 5x -8) + 7\\\\ (fog)=-8x^2-20x+32+7`

Step two:

fog(-3)= put x= -3 in (fog)(-3)=-8x^2-20x+32+7

`(fog)(-3)=-8x^2-20x+32+7\\\\ (fog)(-3)=-8(-3)^2-20(-3)+32+7\\\\ (fog)(-3)=-8*9+60+32+7\\\\ (fog)(-3)=-72-60+32+7\\\\ (fog)(-3)=-93`