Question
Check if the following functions have an inverse function. If yes, find the inverse function.$f(x)=5 x^2$
✓
Answer
$f(x)=5 x^2=y$ (say)
For two values $(x_1$ and $x_2)$ of $x$, values of the function are equal.
$\therefore f$ is not one-one.
$\therefore f$ does not have an inverse.
For two values $(x_1$ and $x_2)$ of $x$, values of the function are equal.
$\therefore f$ is not one-one.
$\therefore f$ does not have an inverse.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many different five-digit number licence plates can be made if.
- First digit cannot be zero and the repetition of digits is not allowed.
- The first-digit cannot be zero, but the repetition of digits is allowed?
Find the number of distinct words formed from letters in the word INDIAN. How many of them have the two N’s together?
Prove the following : $\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 x}}}=2$ $\cos x$
→Express the following recurring decimals as rational numbers.
$51.0 \overline{2}$
→$51.0 \overline{2}$
Evaluate the following limits:
$\lim _{x \rightarrow 0}\left[\frac{(1-x)^5-1}{(1-x)^3-1}\right]$
→$\lim _{x \rightarrow 0}\left[\frac{(1-x)^5-1}{(1-x)^3-1}\right]$
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Verify,
A × (B ∩ C) = (A × B) ∩ (A × C)
Find the radian measure corresponding to the following degree measures:
-47°30'
-47°30'
Find the area of triangle whose vertices are $A(3,7) B(4,-3)$ and $C(5,-13)$. Interpret your answer.
→If $f(x)=\frac{5^x+5^{-x}-2}{x^2}$, for $x \neq 0$
$=k_{\text {, }}$ for $x=0$
is continuous at $x=0$, then find $k$.
→$=k_{\text {, }}$ for $x=0$
is continuous at $x=0$, then find $k$.
If $A=\left[\begin{array}{cc}8 & 4 \\ 10 & 5\end{array}\right], B=\left[\begin{array}{cc}5 & -4 \\ 10 & -8\end{array}\right]$, show that $(A+B)^2=A^2+A B+B^2$.
→