The graph of f inverse, y = f^-1 (x), is the reflection of the graph of y = f(x)

Question

The graph of f inverse, y = f^-1 (x), is the reflection of the graph of y = f(x) across. A. The origin B. The line y = x C. the x - axis D. the y - axis E. none of these Find the inverse of f(x) = 3x +2. A. f^-1 (x) = x + 2/3 B. f^-1 (x) = 2x - 3 C. f^-1 (x) = x - 3/2 D. f^-1(x) = 2x + 3 E. f^-1(x) = x - 2/3 The graph of f(x) = a^x-1 +5 (a > 0, a notequalto 1) has a horizontal asymptote given by the equation... A. y = 5 B. y = 1 C. y = 0 D. y = -1 E. none of these The population of a country doubled in 41 years. What was the approximate exponential growth rate? A. 5.9% B. 4.8% C. 2.1% D. 1.7% E. 1.9%

Explanation / Answer

(41). Answer is B. It's a fact that inverse graph of any graph is reflection of that graph across y = f(x).

(42). f(x) = 3x + 2

Let y = f(x)

So x = f-1(y)

Now y = 3x + 2

y - 2 = 3x

x = y-2/3

Put x = f-1(y)

f-1(y) = y-2/3

Replace y by x then,

f-1(x) = x-2/3

(c). y = ax-1 + 5

Now for horizontal asymptote dy/dx = 0.

So ax-1log(a) = 0

now a>0 so ax-1 = 0

now from question ax-1 = y-5

So. y - 5 = 0

y = 5

(d).

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