Question

For the real valued functions f(x) = x-4/x-5 and g(x) = 4x+17, find the composition fog and specify its domain using interval notation.
(F o g)(x)=
Domain of f o g:

Answer 1

Answer:

(f o g)(x) = $\frac{4x+13}{4x+12}$

Domain : (-∞, -3) ∪ (-3, ∞)

Step-by-step explanation:

Given : f(x) = $\frac{x-4}{x-5}$

            g(x) = 4x + 17

We have to find the value of (f o g)(x).

Since (f o g)(x) = f[g(x)]

                        = $\frac{(4x+17)-4}{(4x+17)-5}$

                        = $\frac{4x+13}{4x+12}$

For the Domain of the function (f o g)(x),

Given function is defined for (4x + 12) ≠ 0

4x ≠ -12

x ≠ -3

Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)