Solve the composition

Question

Part A: Let f(x)= 4- (minus) the square root of x^2+1

and g(x)=x-7

then f(g(x))=?

 

Part B: leave answer in exact (non-decimal) form f(g(x)).

Answer 1

f(g(x)) = 4-sqr(g(x)^2+1) =

4-sqr((x-7)^2 + 1) =

4-sqr(x^2 -14x +14 + 1) =

4-sqr(x^2 -14+ 15)