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Title: Linear Functions

Grade: 1400-a Lesson: S1-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the inverse of a linear function f(x) = 4x + 5.
2	Step	To find the inverse of a linear function, we’ll swap the x and y variables and solve for y.
3	Step	Given the linear function	f(x) = 4x + 5
4	Hint	let’s replace f(x) with y	y = 4x + 5
5	Step	Let’s switch the x and y variables and move the constant term to the left side	x = 4y + 5 x - 5 = 4y
6	Step	Divide both sides by 4	\$("x" - 5)/4 = (4"y")/4\$ \$"y" = ("x" - 5)/4\$
7	Step	Therefore, the inverse of the linear function f(x) = 4x + 5 is: \$"f"^(-1)("x") = ("x" - 5)/4\$.
8	Choice.A	This option has an incorrect intercept; it should be -5 instead of +5 for the inverse function	\$"f"^(-1)("x") = ("x" + 5)/4 \$
9	Choice.B	This option has a different slope and an incorrect intercept, making it the wrong choice for the inverse function	\$"f"^(-1)("x") = ("x" - 4) / 5 \$
10	Choice.C	This option correctly represents the inverse function with the right slope and intercept	\$ "f"^(-1)("x") = ("x" - 5)/4 \$
11	Choice.D	This option suggests adding 4 and dividing by 5, resulting in an incorrect slope and intercept	\$ "f"^(-1) ("x") = ("x" + 4)/5 \$
12	Answer	Option	C
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the inverse of a linear function f(x) = 4x + 5.

Step

To find the inverse of a linear function, we’ll swap the x and y variables and solve for y.

Step

Given the linear function

f(x) = 4x + 5

Hint

let’s replace f(x) with y

y = 4x + 5

Step

Let’s switch the x and y variables and move the constant term to the left side

x = 4y + 5
x - 5 = 4y

Step

Divide both sides by 4

\$("x" - 5)/4 = (4"y")/4\$

\$"y" = ("x" - 5)/4\$

Step

Therefore, the inverse of the linear function f(x) = 4x + 5 is: \$"f"^(-1)("x") = ("x" - 5)/4\$.

Choice.A

This option has an incorrect intercept; it should be -5 instead of +5 for the inverse function

\$"f"^(-1)("x") = ("x" + 5)/4 \$

Choice.B

This option has a different slope and an incorrect intercept, making it the wrong choice for the inverse function

\$"f"^(-1)("x") = ("x" - 4) / 5 \$

Choice.C

This option correctly represents the inverse function with the right slope and intercept

\$ "f"^(-1)("x") = ("x" - 5)/4 \$

Choice.D

This option suggests adding 4 and dividing by 5, resulting in an incorrect slope and intercept

\$ "f"^(-1) ("x") = ("x" + 4)/5 \$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?