Respuesta :

Answer:

[tex]f^{-1}(8)=\frac{3}{2}[/tex]

Step-by-step explanation:

Given f(x)=[tex]2x+5[/tex]

We have to find [tex]f^{-1}(8)[/tex]

In order to find [tex]f^{-1}(x)[/tex] we have to make x as the subject of the formula

Let us assume f(x)=y

⇒[tex]2x+5=y[/tex]

Subtracting both sides by 5

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

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

Dividing both sides by 2

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

⇒[tex]x=\frac{y-5}{2}[/tex]

Now substituting y with x

we have [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Now [tex]f^{-1}(8)=\frac{8-5}{2}[/tex]

=[tex]\frac{3}{2}[/tex]

So option (ii) is correct


zainebamir540

Answer:

Choice B is correct answer.

Step-by-step explanation:

From question statement , we observe that

A function is given and we have to find inverse of this function. Then, we have to find the f⁻¹(8).

f(x) = 2x+5

put f(x) = y in above equation, we get

y = 2x+5

adding -5 to both sides of above equation,we get

y-5 = 2x+5-5

y-5 = 2x

dividing by 2 to both sides of equation,we get

y-5 / 2 = 2x/ 2

y-5 / 2 = x

swapping equation,we get

x = y-5 / 2

put f⁻¹(y) = x in above equation,we get

f⁻¹(y) = y-5 / 2

replace y with x in above equation

f⁻¹(x) = x-5 / 2

we have to find  f⁻¹(8) .

putting x = 8 in above equation,we get

f⁻¹(8) = 8-5/2

f⁻¹(8) = 3/2 which is the answer.