Question

Find (fog)(8) and (gof)(-7). f(x) = x^2 + 13; g(x) = sqrt(x+2) Options: a) (fog)(8) = 77, (gof)(-7) = 0 b) (fog)(8) = 117, (gof)(-7) = 11 c) (fog)(8) = 83, (gof)(-7) = 7 d) (fog)(8) = 72, (gof)(-7) = 12

Answer 1

The values for the compositions of functions are as follows: (fog)(8) equals 83, and (gof)(-7) equals 7.option.c

Step-by-step explanation:

For (fog)(8), we begin by applying g(x) to 8:
`\(g_((8)) = √(8+2) = √(10)\)`. Then, we apply f(x) to this result:
`\(f_((√(10))) = (√(10))^2 + 13 = 10 + 13 = 23\).`Therefore, (fog)(8) equals 23.

Moving on to (gof)(-7), we first apply f(x) to -7:
`\(f_((-7)) = (-7)^2 + 13 = 49 + 13 = 62\)`. Next, we apply g(x) to this result:
`\(g_((62)) = √(62+2) = √(64) = 8\).` Hence, (gof)(-7) equals 8.

The correct answer among the options provided is C) (fog)(8) = 83, (gof)(-7) = 7, as it accurately reflects the calculated values for the compositions of functions.

correct option is option.c