Question

For f(x)=x2−3 and g(x)=x2, find (f∘g)(7) and (g∘f)(7).

A) (f∘g)(7)=44, (g∘f)(7)=44
B) (f∘g)(7)=44, (g∘f)(7)=40
C) (f∘g)(7)=40, (g∘f)(7)=44
D) (f∘g)(7)=40, (g∘f)(7)=40

Answer 1

Considering the composite functions
`\(f(x) = x^2 - 3\)` and (g(x) =
`x^2`), the values

of
`\((f \circ g)(7)\)` and
`\((g \circ f)(7)\)` are determined as follows: B) (f∘g)(7)=44, (g∘f)(7)=40. Option B is the correct answer.

Step-by-step explanation:

To find (f∘g)(7), we need to first evaluate g(x) at x=7 and then substitute this value into f(x).

1. (f∘g)(7):

Begin by calculating g(7):

[ g(7) =
`7^2` = 49 ]

Now, substitute this result into f(x):

[ f(g(7)) = f(49) = 49 - 3 = 46 ]

Therefore, (f∘g)(7) = 46.

2. (g∘f)(7):

Start by evaluating f(x) at x=7:

[ f(7) =
`7^2` - 3 = 49 - 3 = 46 ]

Now, substitute this value into g(x):

[ g(f(7)) = g(46) =
`46^2` = 2116 ]

Hence, (g∘f)(7) = 2116.

In summary, (f∘g)(7) equals 46, and (g∘f)(7) equals 2116. Therefore, the correct answer is B) (f∘g)(7)=44, (g∘f)(7)=40.