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Which function below is the inverse of f(x) = the quantity of two x plus three, over five.?f−1(x) = the quantity of five x plus three, over twof−1(x) = the quantity of five x minus three, over twof−1(x) = five over the quantity of two x plus threef−1(x) = five over the quantity of three minus two x?

Respuesta :

Original function: f(x)=(2x+3)/5
[change f(x) to y]: y=(2x+3)/5
[swap x and y]: x=(2y+3)/5
[solve again for y]: 5x=2y+3
y=(5x-3)/2
f-1(x) = (5x-3)/2..."The quantity five x minus three, over two
isyllus

Answer:

[tex]f^{-1}(x)=\dfrac{5x-3}{2}[/tex]

f⁻¹(x) = the quantity of five x minus three, over two

C is correct

Step-by-step explanation:

Given: [tex]f(x)=\dfrac{2x+3}{5}[/tex]

We need to find inverse of function f(x)

Step 1:  Set f(x)=y

[tex]y=\dfrac{2x+3}{5}[/tex]

Step 2: Switch x and y

[tex]x=\dfrac{2y+3}{5}[/tex]

Step 3: Solve for y (isolate y)

[tex]5x=2y+3[/tex]

[tex]2y=5x-3[/tex]

[tex]y=\dfrac{5x-3}{2}[/tex]

Therefore, [tex]f^{-1}(x)=\dfrac{5x-3}{2}[/tex]

Now we write as sentence form,

Inverse of f(x) is 5 times of x minus 3 over 2.

Hence, f⁻¹(x) = the quantity of five x minus three, over two

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