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Byju's Answer

Standard XII

Mathematics

Properties of Composite Function

If fx = 1 -...

Question

If $f (x) = 1 - 4 x$ , and $f^{- 1} (x)$ is the inverse of $f (x)$ , then the value of $f (- 3) f - 1 (- 3) =$ is:

1

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13

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Solution

The correct option is E $13$
Let $f (x) = 1 - 4 x = y$
$∴ x = \frac{(1 - y)}{4}$ and $x = f^{- 1} (y)$
Therefore $x = f^{- 1} (y) = \frac{(1 - y)}{4}$
So, $f (- 3) f^{- 1} (- 3) = \frac{(1 + 12) (1 + 3)}{4} = 13$

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Consider $f : R - {- \frac{4}{3}} \to R - {\frac{4}{3}}$ given by $f (x) = \frac{4 x + 3}{3 x + 4}$ .Show that f is bijective.Find the inverse of f and Hence find $f^{- 1} (0)$ and x such that $f^{- 1} (x) = 2$ .

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f : R - {- \frac{4}{3}} \to R - {\frac{4}{3}}

given by

f (x) = \frac{4 x + 3}{3 x + 4}

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and hence find

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and

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such that

f^{- 1} (x) = 2

Q. Consider

f : R - {- \frac{4}{3}} \to R - {\frac{4}{3}}

given by

f (x) = \frac{4 x + 3}{3 x + 4}

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and hence find

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The inverse of the real function f(x) = $\frac{4 x}{3 x + 4}$ , $x \neq \frac{- 4}{3}$ ,is f^-1(x) =

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If f(x)=1−4x, and f−1(x) is the inverse of f(x), then the value of f(−3)f−1(−3)= is:

The correct option is E 13Let f(x)=1−4x=y ∴x=(1−y)4 and x=f−1(y)Therefore x=f−1(y)=(1−y)4So, f(−3)f−1(−3)=(1+12)(1+3)4=13

If $f (x) = 1 - 4 x$ , and $f^{- 1} (x)$ is the inverse of $f (x)$ , then the value of $f (- 3) f - 1 (- 3) =$ is:

The correct option is E $13$
Let $f (x) = 1 - 4 x = y$
$∴ x = \frac{(1 - y)}{4}$ and $x = f^{- 1} (y)$
Therefore $x = f^{- 1} (y) = \frac{(1 - y)}{4}$
So, $f (- 3) f^{- 1} (- 3) = \frac{(1 + 12) (1 + 3)}{4} = 13$