F(x) = 3x + 1
let f(x) = y
y = 3x + 1
y - 1 = 3x
3x = y - 1
x = (y - 1)/3
From y = f(x), x = f⁻¹(y)
<span>x = (y - 1)/3
</span>
f⁻¹(y) = (y - 1)/3
f⁻¹(7) = <span>(7 - 1)/3 = 6/3 = 2
</span>f⁻¹(7)<span> = 2</span>
Answer:
Each shirt cost $<u>7</u> and each pair of shorts cost $<u>17</u> .
Step-by-step explanation:
let shirts be represented as x
let shorts be represented as y
Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.
4 x + 3 y = $79 .......equation 1
Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.
7 x + 8 y = $185 .......equation 2
multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.
7 × (4 x + 3 y = $79) ⇒ +28 x + 21 y = $553
-4 × (7 x + 8 y = $185) ⇒ <u> -28 x - 32 y = - $740</u>
0 - 11 y = - $187 ⇒ -11 y = - $187
y =
⇒ y = $17
shorts = y = $17
put value of y in equation 1
4 x + 3 ( $17 ) = $79 ⇒ 4x + $51 = $79 ⇒ 4x = $79 - $51
4x = $28 ⇒ x =
⇒ x = $7
Shirts = x = $7
Answer:
10-2x
Step-by-step explanation:
If x is the length of one side of the square, the total width of the cardboard has two squares cut from it. The amount of width remaining is the width of the box. Since the original width of the cardboard is 10, the width of the box is ...
10 -2x