Verified answer

f(x) = 7x + 2

g(x) = 8 - x^2

f(0) = 7*0 + 2 = 0 + 2 = 2

g(0) = 8 - 0^2 = 8 - 0 = 8

f(g(0)) = f(8) = 7*8 + 2 = 56 + 2 = 58

g(f(0)) = g(2) = 8 - 2^2 = 8 - 4 = 4

You basically just have to throw the one equation into the other like this:

a) f(g(0)) = f(8 - (0)2) = 7(8 - 0(2)) + 2 = 56 +2 = 58

b) g(f(0)) = g(7(0) + 2) = 8 - (7(0) + 2)2 = 8 - 4 = 4

(a) f (g(0))

first plug in 0 for g(x) so g(0)= 8 - 0^2 =8

then take that 8 and plug it in f(x) so f(8) = 7(8) +2 = 58

b. g (f(0))

first plug in 0 for f(x) so f(0) = 7(0)+2 = 2

then take the 2 and plug it in g(x) so g(2) = 8 - (2)^2 = 4

(a) f(g(0)) = 7(8 - x^2) + 2

= 56 - 7x^2 + 2

= 58 - 7x^2

= 58 - 7(0)^2

= 58 answer//

(b) g(f(0)) = 8 - (7x + 2)^2

= 8 - (49x^2+28 x+4)

= 8 - 49x^2 - 28x - 4

=- 49x^2 - 28x + 4

= - 49(0) - 28(0) + 4

= 4 answer//

f(0) = 2

Assuming you mean g(x) = 8 - x² (also written x^2 when superscripts are unavailable), then

g(f(0)) = g(2) = 4

Likewise, g(0) = 8 and f(g(0)) = f(8) = 58