Prove that the function f : R → R defined by f (x) = 2x + 5 is on… - Vidyadip

Question

Prove that the function $f : R → R$ defined by $f (x) = 2x + 5$ is one-one.

✓

Answer

Note that a function $f$ is one-one if
$f\left(x_1\right)=f\left(x_2\right) \Rightarrow x_1=x_2 \text { (definition of one-one function) }$
Now, given that $f\left(x_1\right)=f\left(x_2\right)$, i.e., $2 x_1+5=2 x_2+5$
$\Rightarrow 2 x_1+5-5=2 x_2+5-5$ (adding the same quantity on both sides)
$2 \mathrm{x}_1+0=2 \mathrm{x}_2+0$
$2 x_1=2 x_2$ (using additive identity of real number)
$\frac{2}{2} x_1=\frac{2}{2} x_2$ dividing by the same non zero quantity $\mathrm{x}_1=\mathrm{x}_2$
Hence, the given function is one one

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 "3 Marks Question" from Appendix 1→Appendix 1 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Assume that the chances of a patient having heart attack is 40%. It is also assumed that meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options and patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Find the equations of the planes that passes through three points.
$(1, 1, 0), (1, 2, 1), (-2, 2, -1)$

Find the length of the perpendicular drow from the point (5, 4, -1) to the line $\vec{\text{r}}=\hat{\text{i}}+\lambda\big(2\hat{\text{i}}+9\hat{\text{j}}+5\hat{\text{k}}\big).$

Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}-\text{B})^\text{T}=\text{A}^\text{T}-\text{B}^\text{T}$

Write the equation of the plane whose intercepts on the coordinate axes are 2, -3 and 4

Differentiate the following functions with respect to x:
$10^{(10^\text{x})}$

Sand is being poured onto a conical pile at the constant rate of $50cm^3/ minute$ such that the height of the cone is always one half of the radius of its base. How fast is the height of the pile increasing when the sand is 5cm deep.

The probability is 0.02 that an item produced by a factory is defective. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.

Find the angle between the line $\vec{\text{r}}=(2\hat{\text{i}}+3\hat{\text{j}}+9\hat{\text{k}})+\lambda(2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}})$ and the plane $\vec{\text{r}}\cdot(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})=5$

Write the derivative of $f(x) = |x|^3$ at $x = 0$.