Solved on Jan 25, 2024

Find the value of $x$ that makes the exponent of $f(x)=2^{x-1}$ zero.

STEP 1

Assumptions
1. We are graphing the function $f(x) = 2^{x-1}$ .
2. We want to find the value of $x$ that makes the exponent zero, which is a key point for graphing the function.

STEP 2

To find the value of $x$ that makes the exponent zero, we need to solve the equation $x - 1 = 0$ .

STEP 3

Add 1 to both sides of the equation to isolate $x$ .
$x - 1 + 1 = 0 + 1$

STEP 4

Simplify both sides of the equation.
$x = 1$

STEP 5

Check the result by substituting $x = 1$ back into the exponent of the function.
$2^{1-1} = 2^0$

STEP 6

Recall that any non-zero number raised to the power of 0 is 1.
$2^0 = 1$

STEP 7

Since $2^0 = 1$ , our solution $x = 1$ is correct. This means that the point $(1, 1)$ is on the graph of the function $f(x) = 2^{x-1}$ .
The value of $x$ that makes the exponent zero is $x = 1$ .

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Find the value of $x$ that makes the exponent of $f(x)=2^{x-1}$ zero.

STEP 1

Assumptions
1. We are graphing the function $f(x) = 2^{x-1}$ .
2. We want to find the value of $x$ that makes the exponent zero, which is a key point for graphing the function.

STEP 2

To find the value of $x$ that makes the exponent zero, we need to solve the equation $x - 1 = 0$ .

STEP 3

Add 1 to both sides of the equation to isolate $x$ .
$x - 1 + 1 = 0 + 1$

STEP 4

Simplify both sides of the equation.
$x = 1$

STEP 5

Check the result by substituting $x = 1$ back into the exponent of the function.
$2^{1-1} = 2^0$

STEP 6

Recall that any non-zero number raised to the power of 0 is 1.
$2^0 = 1$

STEP 7

Since $2^0 = 1$ , our solution $x = 1$ is correct. This means that the point $(1, 1)$ is on the graph of the function $f(x) = 2^{x-1}$ .
The value of $x$ that makes the exponent zero is $x = 1$ .

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Find the value of xxx that makes the exponent of f(x)=2x−1f(x)=2^{x-1}f(x)=2x−1 zero.

STEP 1

Assumptions1. We are graphing the function f(x)=2x−1f(x) = 2^{x-1}f(x)=2x−1.2. We want to find the value of xxx that makes the exponent zero, which is a key point for graphing the function.

STEP 2

To find the value of xxx that makes the exponent zero, we need to solve the equation x−1=0x - 1 = 0x−1=0.

STEP 3

Add 1 to both sides of the equation to isolate xxx.x−1+1=0+1x - 1 + 1 = 0 + 1x−1+1=0+1

STEP 4

Simplify both sides of the equation.x=1x = 1x=1

STEP 5

Check the result by substituting x=1x = 1x=1 back into the exponent of the function.21−1=202^{1-1} = 2^021−1=20

STEP 6

Recall that any non-zero number raised to the power of 0 is 1.20=12^0 = 120=1

STEP 7

Since 20=12^0 = 120=1, our solution x=1x = 1x=1 is correct. This means that the point (1,1)(1, 1)(1,1) is on the graph of the function f(x)=2x−1f(x) = 2^{x-1}f(x)=2x−1.The value of xxx that makes the exponent zero is x=1x = 1x=1.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ that makes the exponent of $f(x)=2^{x-1}$ zero.

Assumptions
1. We are graphing the function $f(x) = 2^{x-1}$ .
2. We want to find the value of $x$ that makes the exponent zero, which is a key point for graphing the function.

To find the value of $x$ that makes the exponent zero, we need to solve the equation $x - 1 = 0$ .

Add 1 to both sides of the equation to isolate $x$ .
$x - 1 + 1 = 0 + 1$

Simplify both sides of the equation.
$x = 1$

Check the result by substituting $x = 1$ back into the exponent of the function.
$2^{1-1} = 2^0$

Recall that any non-zero number raised to the power of 0 is 1.
$2^0 = 1$

Since $2^0 = 1$ , our solution $x = 1$ is correct. This means that the point $(1, 1)$ is on the graph of the function $f(x) = 2^{x-1}$ .
The value of $x$ that makes the exponent zero is $x = 1$ .