Question

The function f is defined by f(x) = (x − 2) 2 − 3 for x > −2. The function g is defined by g(x) = 2x+6 x−2 for x > 2. Find fg(7).

Answer 1

Answer:

$fg(7)=143.95$

Step-by-step explanation:

We are given that

$f(x) = (x -2)^2 -3$ for x > −2

$g(x) = 2x+6x^{-2}$ for x > 2

We have to find fg(7)

$fg(7)=f(g(7))$

$=f(2(7)+6(7)^{-2})$

=$f(14+\frac{6}{49})$

=$f(\frac{692}{49})$

692/49>-2

fg(7)=$(\frac{692}{49}-2)^2-3$

=$146.95-3$

Hence, $fg(7)=143.95$