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(x₁ ) = f (x₂ ) $\Rightarrow$ x₁ = x₂ (definition of one-one function)
Now, given that f (x₁ ) = f (x₂ ), i.e., 2x₁ + 5 = 2x₂ + 5
$\Rightarrow$ 2x₁ + 5 – 5 = 2x₂ + 5 – 5 (adding the same quantity on both sides)
2x₁ + 0 = 2x₂ + 0
2x₁ = 2x₂( using additive identity of real number)
$\frac{2}{2} x_{1}=\frac{2}{2} x_{2}$ dividing by the same non zero quantity
x₁ = x₂
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" 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

A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?

Evaluate the following integrals:
$\int^\limits4_{-4}|\text{x}+2|\text{dx}$

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain. A grade and 20% of day scholars attain A grade in their annual examination. At the end of year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

If $\text{y}=\text{e}^{\text{a}\cos^{-1}}\text{x}$ prove that $(1-\text{x}^2)\frac{\text{d}^2\text{y}}{\text{dx}^2}-\text{x}\frac{\text{dy}}{\text{dx}}-\text{a}^2\text{y}=0$

If $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right] \& I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] ;$ Find k, So that $\mathrm{A}^2=\mathrm{kA}$ - 2l.

Differentiate (x²– 5x + 8) (x³ + 7x + 9) in three ways mentioned below:
by using product rule

Let n be a fixed positive integer. Define a relation R in Z as follows $\forall\ \text{a},\ \text{b}\in\text{Z},$ aRb if and only if a - b is divisible by n. Show that R is an equivalance relation.

Solve the following: $\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$.

Evaluate the following integrals:
$\int\sqrt{\text{x}}\Big(\text{x}^3-\frac{2}{\text{x}}\Big)\text{dx}$

Find the value of x if the area of $\triangle$ is 35 square cms with vertices (x, 4), (2, -6) and (5, 4).