Question

Find f(g(-1)) for the pair of functions.
f(x)=x^2+6
g(x)=3x^2-9

Answer 1

• f(x)=x^2+6
• g(x)=3x^2-9

First we have to find g(x) at -1

`\\ \sf\longmapsto g(-1)`

`\\ \sf\longmapsto 3(-1)^2-9`

`\\ \sf\longmapsto 3(1)-9`

`\\ \sf\longmapsto 3-9`

`\\ \sf\longmapsto -6`

Now

`\\ \sf\longmapsto f(-6)`

`\\ \sf\longmapsto (-6)^2+6`

`\\ \sf\longmapsto 36+6`

`\\ \sf\longmapsto 42`

Answer 2

• 42

Explanation:

Given:

• f(x) = x² + 6
• g(x) = 3x² - 9

Find g(-1):

• g(-1) = 3(-1)² - 9 = 3 - 9 = -6

Find f(-6):

• f(-6) = (-6)² + 6 = 36 + 6 = 42