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DEAMER WS 2.13C INVERSE OF LOG FUNCTIONS AND INEQUALITIES (4/14/2026)

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Worksheet C: (Topic 2.13) Exp. and Log. Inverses and Inequalities

Directions: No Calculators Allowed. Find the inverse of the following functions. Be sure to use proper notation.

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1.

Find the inverse of the function $f(x) = 3^{x - 2} + 1$.

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2.

Find the inverse of the function $g(x) = 4(2)^{3x} - 5$.

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3.

Find the inverse of the function $h(x) = \dfrac{1}{5} e^{2x + 3}$.

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4.

Find the inverse of the function $k(x) = 3 \log(x + 1) - 2$.

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5.

Find the inverse of the function $p(x) = -4 \ln(2x)$.

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6.

Find the inverse of the function $m(x) = 2 - \log_{3}\!\left(\dfrac{x}{4}\right)$.

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7.

Let $f(x) = 4(2)^{{5x - 6}{}} + 3$ and let $g(x) = f^{-1}(x)$. For what value of $x$ does $g(x) = 1$?

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8.

Let $h(x) = 5 - 2(3)^{7 - x}$ and let $k(x) = h^{-1}(x)$. For what value of $x$ does $k(x) = 5$?

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9.

Let $p(x) = 3 \ln(2x - 1)$ and let $m(x) = p^{-1}(x)$. For what value of $x$ does $m(x) = 3$?

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10.

Let $f(x) = \log_{3}(x^{2} + x + 2) - \log_{3}(x + 6)$. What are all the values of $x$ for which $f(x) < 0$?

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11.

Let $g(x) = \log(x^{2} + 3x - 5) - \log(7x + 16)$. What are all the values of $x$ for which $g(x) > 0$?

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12.

Let $h(x) = \ln(x^{2} + 5)$ and let $k(x) = \ln(7x - 7)$. What are all values of $x$ for which $h(x) > k(x)$?

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13.

Let $p(x) = 12 + 5(3)^{4x + 1}$. What are all the values of $x$ for which $p(x) \ge 57$?

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14.

(Challenge) Let $f(x) = \log_{2}(x^{2} + 10x + 24) - \log_{2}(2x - 1)$. What are all values of $x$ for which $f(x) > 3$?