Question

Given that f(x)=x^(2)-14 and g(x)=9-x, find (f-g)(6), if it exists.

Answer 1

f(x)=x^2-14

g(x)=9-x

Find g(6)

`\\ \sf\longmapsto g(6)=9-6=3`

Now

`\\ \sf\longmapsto (f-g)(x)=f(g(x))`

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

`\\ \sf\longmapsto f(3)`

`\\ \sf\longmapsto 3^2-14`

`\\ \sf\longmapsto 9-14`

`\\ \sf\longmapsto -5`

Answer 2

• -5

Explanation:

Given:

• f(x) = x² - 14 and g(x) = 9 - x

Find (f-g)(6):

• g(6) = 9 - 6 = 3
• (f-g)(6) = f(g(6)) = f(3) = 3² - 14 = 9 - 14 = -5