Math / Algebra

Question(a) The value of $f(1)$ is about 110 . (Round to the nearest whole number as needed.) (b) The value of $f^{-1}(110)$ is about $\square$ (Round to the nearest whole number as needed.)

Studdy Solution

STEP 1

What is this asking? If $f(1)$ is about 110, what's the value of $f^{-1}(110)$ ? Watch out! Don't mix up the function and its inverse!

STEP 2

1. Understand Inverse Functions
2. Apply the Concept

STEP 3

Alright, awesome students, let's break down what an inverse function actually means!
If we have a function, let's call it $f(x)$ , and we plug in a value, let's say $x = a$ , and it spits out a value, let's call it $b$ , so $f(a) = b$ , then the inverse function, written as $f^{-1}(x)$ , reverses this process!

STEP 4

So, if $f(a) = b$ , then $f^{-1}(b) = a$ .
It's like a magical undo button!
We put $b$ into the inverse function, and it gives us back the original $a$ .

STEP 5

The problem tells us that $f(1)$ is about $\textbf{110}$ .
This means when we plug in $x = \textbf{1}$ into our function $f(x)$ , it gives us $\textbf{110}$ .
So, we have $f(\textbf{1}) = \textbf{110}$ .

STEP 6

Now, we want to find $f^{-1}(\textbf{110})$ .
Remember what we learned about inverse functions?
They reverse the process!
Since $f(\textbf{1}) = \textbf{110}$ , then $f^{-1}(\textbf{110}) = \textbf{1}$ .
It's as simple as that!

STEP 7

$f^{-1}(110)$ is about $\textbf{1}$ .

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Question(a) The value of $f(1)$ is about 110 . (Round to the nearest whole number as needed.) (b) The value of $f^{-1}(110)$ is about $\square$ (Round to the nearest whole number as needed.)

Studdy Solution

STEP 1

What is this asking? If $f(1)$ is about 110, what's the value of $f^{-1}(110)$ ? Watch out! Don't mix up the function and its inverse!

STEP 2

1. Understand Inverse Functions
2. Apply the Concept

STEP 3

STEP 4

So, if $f(a) = b$ , then $f^{-1}(b) = a$ .
It's like a magical undo button!
We put $b$ into the inverse function, and it gives us back the original $a$ .

STEP 5

The problem tells us that $f(1)$ is about $\textbf{110}$ .
This means when we plug in $x = \textbf{1}$ into our function $f(x)$ , it gives us $\textbf{110}$ .
So, we have $f(\textbf{1}) = \textbf{110}$ .

STEP 6

Now, we want to find $f^{-1}(\textbf{110})$ .
Remember what we learned about inverse functions?
They reverse the process!
Since $f(\textbf{1}) = \textbf{110}$ , then $f^{-1}(\textbf{110}) = \textbf{1}$ .
It's as simple as that!

STEP 7

$f^{-1}(110)$ is about $\textbf{1}$ .

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Question(a) The value of f(1)f(1)f(1) is about 110 . (Round to the nearest whole number as needed.) (b) The value of f−1(110)f^{-1}(110)f−1(110) is about □\square□ (Round to the nearest whole number as needed.)

Studdy Solution

STEP 1

What is this asking? If f(1)f(1)f(1) is about 110, what's the value of f−1(110)f^{-1}(110)f−1(110)? Watch out! Don't mix up the function and its inverse!

STEP 2

1. Understand Inverse Functions2. Apply the Concept

STEP 3

STEP 4

So, if f(a)=bf(a) = bf(a)=b, then f−1(b)=af^{-1}(b) = af−1(b)=a.It's like a magical undo button!We put bbb into the inverse function, and it gives us back the original aaa.

STEP 5

The problem tells us that f(1)f(1)f(1) is about 110\textbf{110}110.This means when we plug in x=1x = \textbf{1}x=1 into our function f(x)f(x)f(x), it gives us 110\textbf{110}110.So, we have f(1)=110f(\textbf{1}) = \textbf{110}f(1)=110.

STEP 6

Now, we want to find f−1(110)f^{-1}(\textbf{110})f−1(110).Remember what we learned about inverse functions?They *reverse* the process!Since f(1)=110f(\textbf{1}) = \textbf{110}f(1)=110, then f−1(110)=1f^{-1}(\textbf{110}) = \textbf{1}f−1(110)=1.It's as simple as that!

STEP 7

f−1(110)f^{-1}(110)f−1(110) is about 1\textbf{1}1.

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Studdy solves anything!

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

Question(a) The value of $f(1)$ is about 110 . (Round to the nearest whole number as needed.) (b) The value of $f^{-1}(110)$ is about $\square$ (Round to the nearest whole number as needed.)

What is this asking? If $f(1)$ is about 110, what's the value of $f^{-1}(110)$ ? Watch out! Don't mix up the function and its inverse!

1. Understand Inverse Functions
2. Apply the Concept

So, if $f(a) = b$ , then $f^{-1}(b) = a$ .
It's like a magical undo button!
We put $b$ into the inverse function, and it gives us back the original $a$ .

The problem tells us that $f(1)$ is about $\textbf{110}$ .
This means when we plug in $x = \textbf{1}$ into our function $f(x)$ , it gives us $\textbf{110}$ .
So, we have $f(\textbf{1}) = \textbf{110}$ .

Now, we want to find $f^{-1}(\textbf{110})$ .
Remember what we learned about inverse functions?
They reverse the process!
Since $f(\textbf{1}) = \textbf{110}$ , then $f^{-1}(\textbf{110}) = \textbf{1}$ .
It's as simple as that!

$f^{-1}(110)$ is about $\textbf{1}$ .