Two functions f and g are defined on the set of real numbers, R, by \(f:x\to x^2+2\) and \(g:x\to \frac{1}{x+2}\).Find the domain of \((g\circ f)^{-1}\)
Question 1 Report
Two functions f and g are defined on the set of real numbers, R, by
\(f:x\to x^2+2\) and \(g:x\to \frac{1}{x+2}\).Find the domain of \((g\circ f)^{-1}\)
Answer Details
f:x → x2 + 2 and g:x → 1x+2.
(g∘f)−1
(g∘f)x2+2
gx2+2 = 1(x2+2)+2
(g∘f) = 1(x2+4
let y = 1(x2+4
y((x2+4) = 1
yx2+4y=1
x2 = 1−4yy
x = 1−4yy−−−−√
(g∘f)−1 = 1−4xx−−−−√
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