2. The functionsf and g are defined as below. f(x) = 3x+2: XER g(x)= 6 2x +3 Find the value of x for which f(g(x)) = 3 Sketch in a single diagram, the graphs of f(x) and f(x). Express each of f(x) and g(x), and solve the equation f¹(x) = g(x)
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Expert's answer
2021-11-22T15:55:18-0500
f(x)=3x+2,x∈R
g(x)=2x+36,x∈R,x=−1.5
(i)
f(g(x))=3(2x+36)+2
Given
f(g(x))=3
3(2x+36)+2=3
2x+318=1
2x+3=18
2x=15
x=7.5
(ii)
f(x)=3x+2
Replace f(x) with y
y=3x+2
Interchange x and y
x=3y+2
Solve for y
y=31x−32
Replace y with f−1(x)
f−1(x)=31x−32
The graph of a function and its inverse are symmetric with respect to the line y=x.
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