Question

10. Given that f(x)=5x-4/3, find
a) f-1(x)​

Answer 1

Answer:

12th

Maths

Continuity and Differentiability

Continuity

The values of b for which t...

MATHS

The values of b for which the function

f(x)={

5x−4,0<x≤1

4x

2

+3bx,1<x<2

is continuous at every point of its domain is

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ANSWER

Given, f(x)={

5x−4,0<x≤1

4x

2

+3bx,1<x<2

is continuous at every point of its domain.

f(x) is continuous.

⇒L.H.L=R.H.L=f(1)

⇒lim

x→1

5x−4=lim

x→1

4x

2

+3bx=1

⇒1=4+3b=1

⇒3b=−3

∴b=−1

Hence, option A.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let y= f(x)

then

$y = 5x - \frac{4}{3} \\ now \: \: calculate \: \: the \: \: value \: \: of \: \: x \\ 5x = y + \frac{4}{3} \\ x = \frac{y}{5} + \frac{4}{15} \\ it \: \: is \: called \: \: inverse \: \: function \: \\ replace \: \: y \: \: with \: \: x \\ we \: \: get\\ \\ f ^{ - 1} (x) = \frac{x}{5} + \frac{4}{15}$