Question:
If $f: R \to R$ is defined by $f(x) = 3x - 4$, then $f^{-1(x)$ is:
If $f: R \to R$ is defined by $f(x) = 3x - 4$, then $f^{-1(x)$ is:
Show Hint
The inverse function undoes the operations of the original function in reverse order.
Updated On: Apr 8, 2026
- $\frac{x+4}{3}$
- $\frac{x-4}{3}$
- $3x+4$
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept
To find the inverse, set $y = f(x)$ and solve for $x$ in terms of $y$.
Step 2: Analysis
$y = 3x - 4 \Rightarrow y + 4 = 3x \Rightarrow x = \frac{y+4}{3}$.
Step 3: Conclusion
Replacing $y$ with $x$, we get $f^{-1}(x) = \frac{x+4}{3}$.
Final Answer: (A)
To find the inverse, set $y = f(x)$ and solve for $x$ in terms of $y$.
Step 2: Analysis
$y = 3x - 4 \Rightarrow y + 4 = 3x \Rightarrow x = \frac{y+4}{3}$.
Step 3: Conclusion
Replacing $y$ with $x$, we get $f^{-1}(x) = \frac{x+4}{3}$.
Final Answer: (A)
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET types of functions Questions
- Let \( f:\mathbb{N} \to \mathbb{N} \) be defined as \[ f(n)= \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] Then \( f \) is:
- Let \( f(x) = \frac{1}{\sqrt{1 + x^2}} \), then:
- The function \( f(x) = \max\left\{(1 - x), (1 + x), 2\right\}, \, x \in (-\infty, \infty) \) is equivalent to
- If \( f(x) = \frac{a^x + a^{-x}}{2} \) and \( f(x+y) + f(x-y) = k f(x)f(y) \), then \( k \) is equal to
- A man \(1.6\mathrm{m}\) high walks at the rate of \(30\mathrm{m/min}\) away from a lamp which is \(4\mathrm{m}\) above ground. How fast is the man's shadow lengthening?
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions