2.10 · Inverses of Exponential Functions

Try each one on paper first, then tap to check.

1. 1.

   Exponential, logarithmic, or neither? Why? Find points for the inverse $g$.

   $x$	$f(x)$
   $3$	$8$
   $4$	$16$
   $5$	$32$
   $6$	$64$

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2. 2.

   Exponential, logarithmic, or neither? Why? Find points for the inverse $g$.

   $x$	$f(x)$
   $\tfrac19$	$-2$
   $\tfrac13$	$-1$
   $1$	$0$
   $3$	$1$

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3. 3.

   Exponential, logarithmic, or neither? Why? Find points for the inverse $g$.

   $x$	$f(x)$
   $0$	$1$
   $1$	$4$
   $2$	$7$
   $3$	$10$

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4. 4.

   Graph of $f$ through $(0.5, 1), (1, 0), (2, -1), (4, -2)$. Exponential, logarithmic, or neither? Find points for $g$.
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5. 5.

   Are these inverses? $f(x) = 2\log_2 x$ and $g(x) = 2^{2x}$
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6. 6.

   Are these inverses? $f(x) = 10^{0.25x}$ and $g(x) = 4\log x$
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7. 7.

   Are these inverses? $f(x) = 5^{x/8}$ and $g(x) = 8\log_5 x$
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8. 8.

   Find the inverse: $h(x) = 4^{5x}$
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9. 9.

   Find the inverse: $m(x) = 5\log_2 x$
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10. 10.

    Find the inverse: $a(x) = \tfrac14\log_8 x$
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11. 11.

    Find the inverse: $b(x) = 10^{\frac34 x}$
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12. 12.

    Which could be the inverse of $f(x) = 0.25^x$?
    (A) table: $(-3,64), (-2,16), (-1,4), (0,1)$
    (B) table: $(4,-1), (1,0), (\tfrac14,1), (\tfrac1{16},2)$
    (C) graph: decreasing, vertical asymptote $x=0$, crosses the $x$-axis at $(1,0)$
    (D) graph: decreasing, horizontal asymptote $y=0$, crosses the $y$-axis at $(0,1)$
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