Chapter 5: Q. 91 (page 285)

Suppose that $f (x) = 2^{x}$ .
(a) What is $f (4)$ ? What point is on the graph of f?
(b) If $f (x) = \frac{1}{16}$ , what is x? What point is on the graph of f?

Short Answer

Expert verified

Part (a) $f (4) = 16$ and the point on the graph is $(4, 16)$ .

Part (b) $x = - 4$ and the point on the graph is $(- 4, \frac{1}{16})$ .

Step by step solution

Part (a) Step 1. Substitute x=4 in f(x)=2x.

This gives

$f (4) = 2^{4} f (4) = 16$

So the point on the graph of the function f is $(4, 16)$ .

Part (b) Step 1. Find value of x using f(x)=116.

$f (x) = \frac{1}{16} 2^{x} = \frac{1}{16} 2^{x} = 16^{- 1} 2^{x} = {(2^{4})}^{- 1} 2^{x} = 2^{- 4}$

On comparing,

$x = - 4$

So the point on the graph is $(- 4, \frac{1}{16})$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Suppose that $f (x) = 2^{x}$ .
(a) What is $f (4)$ ? What point is on the graph of f?
(b) If $f (x) = \frac{1}{16}$ , what is x? What point is on the graph of f?

Short Answer

Step by step solution

Part (a) Step 1. Substitute x=4 in f(x)=2x.

Part (b) Step 1. Find value of x using f(x)=116.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Pure Maths

Mechanics Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Suppose that f(x)=2x.(a) What is f(4)? What point is on the graph of f?(b) If f(x)=116, what is x? What point is on the graph of f?

Short Answer

Step by step solution

Part (a) Step 1. Substitute x=4 in f(x)=2x.

Part (b) Step 1. Find value of x using f(x)=116.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Pure Maths

Mechanics Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Suppose that $f (x) = 2^{x}$ .
(a) What is $f (4)$ ? What point is on the graph of f?
(b) If $f (x) = \frac{1}{16}$ , what is x? What point is on the graph of f?