Answers:
a = 3
x intercept = -2
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Step-by-step explanation:
f(x) is the original function given. Let g(x) be the inverse of f(x).
To find the inverse, we first replace f(x) with y to get
y = (1/3)x-2
Afterward, we swap x and y to get
x = (1/3)y-2
From here, we must isolate or solve for y. To do so, add 2 to both sides and then multiply both sides by 3
x = (1/3)y-2
x+2 = (1/3)y
3(x+2) = y
y = 3(x+2)
g(x) = 3(x+2)
This explains where the x+2 comes from in the a(x+2) expression
The value of 'a' is therefore a = 3
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To find the x intercept of the inverse, we replace g(x) with 0 and solve for x
g(x) = 3(x+2)
0 = 3(x+2)
0/3 = x+2
0 = x+2
x+2 = 0
x = 0-2
x = -2
The x intercept is x = -2. Plugging this x value into g(x) leads to g(x) = 0.
The g(x) graph crosses the x axis at x = -2.