Question

Consider the function f(x)=3/4x+12 what is the y-intercept of f-1(x)

Answer 1

Answer:

y = -16

Step-by-step explanation:

f(x)=3/4x+12 (replace f(x) with y)

y =3/4x+12  (rearrange to express x in terms of y)

y - 12=3/4 x

3/4 x = y - 12

3x = 4(y - 12)

x = (4/3)(y - 12)

x = (4/3)y - (4/3)(12)

x = (4/3)y - 16

$f^{-1}$ (y) = (4/3)y - 16

$f^{-1}$ (x) = (4/3)x - 16

comparing to general form

y = mx + b where b is the y-intercept

b = -16

Hence the y-intercept is y = -16

Answer 2

The value of the y-intercept will be given as y = -16

What is an equation?

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

f (x)  = 3/4x  +  12 (replace f(x) with y)

y     =   3/4x  +  12  (rearrange to express x in terms of y)

y - 12  =  3/4 x

3/4 x  =  y - 12

3x    =   4(y - 12)

x     =  (4/3)(y - 12)

x    =    (4/3)y - (4/3)(12)

x    =    (4/3)y - 16

(y)  =  (4/3)y - 16

(x) =   (4/3)x - 16

Compared to the general form

y = mx + b where b is the y-intercept

b = -16

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