Question
Let $f(x)=x^5+2 x-3$. Find $\left(f^{-1}\right)^{\prime}(-3)$.
✓
Answer
Given : $f(x)=x^5+2 x-3$
Diff. w. r.t.x we get,
$
f^{\prime}(x)=5 x^4+2
$
Note that $y=-3$ corresponds to $x=0$.
$
\begin{aligned}
\therefore \quad\left(f^{-1}\right)^{\prime}(-3) & =\frac{1}{f^{\prime}(0)} \\
& =\frac{1}{5(0)+2}=\frac{1}{2}
\end{aligned}
$
Diff. w. r.t.x we get,
$
f^{\prime}(x)=5 x^4+2
$
Note that $y=-3$ corresponds to $x=0$.
$
\begin{aligned}
\therefore \quad\left(f^{-1}\right)^{\prime}(-3) & =\frac{1}{f^{\prime}(0)} \\
& =\frac{1}{5(0)+2}=\frac{1}{2}
\end{aligned}
$
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
Determine the order and degree of the following differential equations:
→$\left(\frac{d^3 y}{d x^3}\right)^2=\sqrt[5]{1+\frac{d y}{d x}}$
A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interest. Using matrix method, find the amount invested by the trust.
State which of the following are not the probability mass function of a random variable. Give reasons for your answer : 
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$(\text{y"})^2+(\text{y})^3+\sin\text{y}=0$
→$(\text{y"})^2+(\text{y})^3+\sin\text{y}=0$
In $\triangle ABC$, prove that $ac\ \cos B − bc \cos\ A = a^2 − b^2$
→ Which of the following equations have no solutions : 3 sin θ = 5
Evaluate the following functions : $\int \frac{\cos \sqrt{x}}{\sqrt{x}} \cdot d x $
→Suppose that $X$ is waiting time in minutes for a bus and its p.d.f. is given by $f(x)=\frac{1}{5}$, for 0 $\leq x \leq 5$ and $=0$ otherwise. Find the probability that
waiting time is between 1 and 3
→waiting time is between 1 and 3
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
$2\text{X}+3\text{Y}=\begin{bmatrix}2&3\\4&0\end{bmatrix},\ 3\text{X}+2\text{Y}\begin{bmatrix}-2&2\\1&-5\end{bmatrix}$
→$2\text{X}+3\text{Y}=\begin{bmatrix}2&3\\4&0\end{bmatrix},\ 3\text{X}+2\text{Y}\begin{bmatrix}-2&2\\1&-5\end{bmatrix}$
Write the degree of the following differrntial equation $ \Big(\frac{\text{dy}}{\text{dx}}\Big)^{4}+3\text{x}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=0.$
→