Provide a correct answer to this problem quickly please.

What is the inverse of the function?<br> f(x) = 1/3x-5

OlgaM077 [116]

Answer:

-1

f (x) = -3(x + 5)

Step-by-step explanation:

1) in f(x) = 1/3x-5, replace f(x)= with y= as follows: y = (1/3)x - 5

2) interchange x and y, obtaining: x = (1/3)y - 5

3) solve this result for y: (1/3)y = -x - 5, or -(x + 5). Next, multiply both sides by 3 to eliminate the fraction (1/3): y = -3(x + 5)

4) replace y with the symbol for "inverse of f(x);

-1

f (x) = -3(x + 5)

5 0

3 years ago

Steve and Conner together have $60. Steve has $9 more than twice Conner’s amount. How much money does each have?

Lapatulllka [165]

Answer:

Step-by-step explanation:

let a=Ann's amt., b=Betty's amt.

a=2b+9

b+2b+9=60

3b+9-9=60-9

3b=51

b=$17

a=34+9=$43

6 0

3 years ago

What’s the vertex form of F(x)=x^2+2x-3

kupik [55]

Answer:

$\large\boxed{f(x)=(x+1)^2-4}$

Step-by-step explanation:

$\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================$

$\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================$

$\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4$