(B) Given $f(x) = 3x - 4$. To find the inverse function ${f^{ - 1}}(x)$,let $y = f(x)$. Then $y = 3x - 4$. Solving for $x$ in terms of $y$: $y + 4 = 3

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(B) Given $f(x) = 3x - 4$. To find the inverse function ${f^{ - 1}}(x)$,let $y = f(x)$. Then $y = 3x - 4$. Solving for $x$ in terms of $y$: $y + 4 = 3x$ $x = \frac{y + 4}{3}$. By definition,if $y = f(x)$,then $x = {f^{ - 1}}(y)$. Therefore,${f^{ - 1}}(y) = \frac{y + 4}{3}$. Replacing $y$ with $x$,we get ${f^{ - 1}}(x) = \frac{x + 4}{3}$.

Class 12 Mathematics Relation and Function Inverse Function

Easy

If $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = 3x - 4$,then ${f^{ - 1}}: \mathbb{R} \to \mathbb{R}$ is

A
$4 - 3x$
B
$\frac{x + 4}{3}$
C
$\frac{1}{3x - 4}$
D
$\frac{3}{x + 4}$

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Relation and Function

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Inverse Function

State with reason whether the following function has an inverse: $f: \{1,2,3,4\} \rightarrow \{10\}$ with $f = \{(1,10), (2,10), (3,10), (4,10)\}$.

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The number of integral values of $a$ for which the function $f: R \to R, f(x) = 2x^3 - 3(a + 2)x^2 + 12ax - 7$ where $a \in [-4, 6]$ is invertible,is

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Let $f(x) = (x + 1)^2 - 1$ for $x \ge -1$. Then the set $S = \{ x : f(x) = f^{-1}(x) \}$ is

DifficultIIT 1995

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The condition for a function $y = f(x)$ to be invertible is that it must be:

Medium

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Let $f(x) = \frac{x^2 - x}{x^2 + 2x}$,$x \ne 0, -2$. Then $\frac{d}{dx}[f^{-1}(x)]$ (wherever it is defined) is equal to

DifficultJEE MAIN 2013

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If $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = 3x - 4$,then ${f^{ - 1}}: \mathbb{R} \to \mathbb{R}$ is

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