Problem

Find the exponential function $ f(x) = Cb^x $ who…

01:51

Problem 20 Medium Difficulty

Find the domain of each function.

(a) $ g(t) = \sqrt{10^t - 100} $
(b) $ g(t) = \sin (e^t - 1) $

Answer

a) Domain : $[2,+\infty)$
b) $(-\infty, \infty)$

Johns Hopkins University

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Video Transcript

to find the domain of this function. Let's concentrate on the quantity inside the square root. We need that quantity to be greater than or equal to zero because that's the only way to get a really output. So we need 10 to the power t minus 100 to be greater than or equal to zero. So 10 to the power T is going to be greater than or equal to 100. Okay, we know that 10 to the second power is 100. So if t is greater than or equal to two, we ought to have numbers that will fit in the domain and will give us a real output. And if we want to put if we want to give this answer using interval notation, we can say to to infinity Now, for part B, we want to find the domain of this function. So if you think about it, the sine function in General Weichel sign of X has the domain, all real numbers. So it really doesn't matter what you end up getting for each of the T minus one. Because no matter what it is, it's going to be the sign of it is going to be riel and e to the T always gives you a real output. Subtracting one from that always gives you a real output on the sign of a real numbers. A real number. So there are no restrictions to the domain. The domain is going to be all real numbers, and you can write that as negative infinity to infinity.

Heather Z.

Oregon State University

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 4

Exponential Functions

Problem

Find the exponential function $ f(x) = Cb^x $ who…

Problem 20 Medium Difficulty

Find the domain of each function.

(a) $ g(t) = \sqrt{10^t - 100} $
(b) $ g(t) = \sin (e^t - 1) $

Answer

a) Domain : $[2,+\infty)$
b) $(-\infty, \infty)$

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Lily A.

Catherine R.

Heather Z.

Samuel H.

Calculus 3 Courses

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

Calculus: Early Transcendentals

Lily A.

Catherine R.

Heather Z.

Samuel H.

Vectors Intro

Vector Basics - Example 1

a) Domain : $[2,+\infty)$b) $(-\infty, \infty)$

Calculus: Early Transcendentals

Lily A.

Catherine R.

Heather Z.

Samuel H.

Vectors Intro

Vector Basics - Example 1

Lily A.

Catherine R.

Heather Z.

Samuel H.

a) Domain : $[2,+\infty)$
b) $(-\infty, \infty)$