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2 years ago

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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 no

tation.
(F o g)(x)=
Domain of f o g:

1 answer:

Studentka2010 [4]2 years ago

3 0

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, ∞)

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