Chapter 2: Q55. (page 62)

If $f (3 a - 1) = 12 a - 7$ , find $f (x)$ .

Short Answer

Expert verified

The required function is $f (x) = 4 x - 3$ .

Step by step solution

– Given information.

The given function is:

$f (3 a - 1) = 12 a - 7$

To find the function $f (x)$ .

– Equate the input values.

$\begin{array}{l} 3 a - 1 = x \\ 3 a = x + 1 \\ a = \frac{x + 1}{3} \end{array}$

– Substitute the value of the variable in the given function.

Substitute $a = \frac{x + 1}{3}$ in the function $f (3 a - 1) = 12 a - 7$ .

$\begin{array}{l} f (3 (\frac{x + 1}{3}) - 1) = 12 (\frac{x + 1}{3}) - 7 \\ f ((x + 1) - 1) = 4 (x + 1) - 7 \\ f (x + 1 - 1) = 4 x + 4 - 7 \\ f (x) = 4 x - 3 \end{array}$

Thus, the required function is $f (x) = 4 x - 3$ .

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If $f (3 a - 1) = 12 a - 7$ , find $f (x)$ .

Short Answer

Step by step solution

– Given information.

– Equate the input values.

– Substitute the value of the variable in the given function.

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If f3a-1=12a-7, find fx.

Short Answer

Step by step solution

– Given information.

– Equate the input values.

– Substitute the value of the variable in the given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Statistics

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

If $f (3 a - 1) = 12 a - 7$ , find $f (x)$ .