Question

Let f(x) = x^2+7 and g(x) = x+ 3 / x. Find (g (circle) f) (-5)

a.) 35/12

b.) 35/32

c.) 32/35

d.) 11/25

I think it is a.

Answer 1

Note:
When writing rational expressions (a polynomial divided by another), it is important to insert parentheses around each of numerator and denominator.
The answers are ALL missing parentheses in the numerator and denominator.
In the question,
g(x)=x+3/x would mean (x)+(3/x) instead of (x+3)/x as it is meant to be.

Now
(g.f)(-5) means g(f(-5)) because the original expression is evaluated from right to left.
Substitute -5 for x in f(x) to find f(-5). I.e. find f(-5)=(-5)^2+7.
Then substitute the result as x in g(x) to find the answer.

Please give it another try, either because of the typo, which affects calculations on a calculator, or you have misinterpreted the meaning of (g.f)(-5).

Answer 2

Find (g (circle) f) (-5) can also be written as
g( f(x) )

the way you typed it:
f(-5) = 25+7 = 32
g(32) = 32 + 3/32
= 1027/32 which is none of the choices

if you meant:
g(x) = (x+3)/x
then g(32)
= 35/32 , which would be b)

What did you do to get a) ??

Answer 3

(g◦f)(-5)
= g(f(-5))
= g((-5)^2+7)
= g(32)
= (32+3)/32
= 35/32

or,

g(f) = (f+3)/f
= (x^2+7+3)/(x^2+7)
= (x^2+10)/(x^2+7)
so,
(g◦f)(-5) = (25+10)/(25+7) = 35/32