If f : R → R be defined by f(x) = x^4, write f^ -1 (1). - Vidyadip

Question

If $f : R → R$ be defined by $f(x) = x^4,$ write $f^{-1}(1).$

✓

Answer

Let $f^{-1}(1) = x ......(1)$
$\Rightarrow f(x) = 1$
$\Rightarrow x^4 = 1$
$\Rightarrow x^4 - 1 = 0$
$\Rightarrow (x^2 - 1)(x^2 + 1) = 0 [$Using identity: $a^2 - b^2 = (a - b)(a + b)]$
$\Rightarrow (x - 1)(x + 1)(x^2 + 1) = 0 [$Using identity: $a^2 - b^2 = (a - b)(a + b)]$
$\Rightarrow\ \text{x}=\pm1\ [\text{as x}\in\text{R}]$
$\Rightarrow f^{-1}(1) = {-1, 1} [$from $(1)]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A be a $3 \times 3$ square matrix, such that $A (adj\ A) = 2I,$ where I is the identity matrix. Write the value of $|adj\ A|.$

Differentiate $x^2$ with respect to $x^3$.

Find that minimum value of a for which the function $f(x)=x^2+a x+1$ is increasing in interval $(1,2)$.

Evalute the following integrals:
$\int\frac{\sec\text{x}\tan\text{x}}{3\sec\text{x}+5}\text{dx}$

Show that $\text{f}(\text{x})=\log_{\text{a}}\text{x},0<\text{a}<1$ is a decreasing function for all x > 0.

Write the value of $\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big).$

Give an example of a relation which is,
Transitive but neither reflexive nor symmetric.

Find the position vector of the mid-point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).

For the principal values, evaluate the following:
$\text{cosec}^{-1}\Big(2\tan\frac{11\pi}{6}\Big)$

Which of the following functions from $A$ to $B$ are one-one and onto$?$
$f_2 = \{(2, a), (3, b), (4, c)\}; A = \{2, 3, 4\}, B = \{a, b, c\}$