If f(x) = 6 - 5x, ƒ : R → R, where R is a set of all real numbers, then f is:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper

Answer 1

Given:

f(x) = 6 - 5x, ƒ : R → R, where R is a set of all real numbers.

Concept:

If f(x1) = f(x2) ⇒ x1 = x2 Then f(x) is one - one function.

Calculation:

f(x) = 6 - 5x, ƒ : R → R, where R is a set of all real numbers.

Let f(x₁) = f(x₂)

⇒ 6 - 5x₁ = 6 - 5x₂

⇒ - 5x₁ = - 5x₂

⇒ x₁= x₂

Hence f(x) is one - one function.

Now, Let y = f(x)

y = 6 - 5x

⇒ 5x = 6 - y

⇒ \(\rm x= \frac{6-y}{5}\)

Put value of x in given function then

\(\rm f(x)= 6-5\left(\frac{6-y}{5}\right)\)

⇒ f(x) = 6 - 6 + y

⇒ f(x) = y

Hence the function f(x) is onto.

Hence the option (3) is correct.

Download Solution PDF