Which of the following statements have the same result? explain each step in solving each one.

i. f(3) when f(x) = 2x + 2
ii. f-1(4) when f(x) = (3x-4)/5
iii. y + 10 = 2y + 1

Answers

Y +5=2y+1 has the same result.
Quick  which of the following statements have the same result?  explain each step in solving each on
F(x) = 2x + 2find f(3)
f(3) = 2(3) + 2
f(3) = 6 + 2
f(3) = 8

f(x) = (3x - 4)/5find f^-1(4)
y = (3x - 4)/5...swap the variables
x = (3y - 4)/5 ...solve for y
5x = 3y - 4
5x + 4 = 3y
(5x + 4)/3 = y
f^-1(x) = (5x + 4)/3for f(4)
f(4) = (5(4) + 4)/3
f(4) = (20 + 4)/3
f(4) = 24/3
f(4) = 8

y + 10 = 2y + 1
y - 2y = 1 - 10
-y = -9
y = 9

so 1 and 2 have the same result...8

None, because 11\neq 9.5\neq 8.

Step-by-step explanation:

I. When f(x)=3x+2, then

f(3)=3\cdot 3+2=9+2=11.

II. Find the inverse function f^{-1}(x) for the function f(x)=\dfrac{2x-7}{3}.

y=\dfrac{2x-7}{3},\\ \\3y=2x-7,\\ \\2x=3y+7,\\ \\x=\dfrac{3y+7}{2},\\ \\f^{-1}(x)=\dfrac{3x+7}{2}.

Thus,

f^{-1}(4)=\dfrac{3\cdot 4+7}{2}=\dfrac{12+7}{2}=\dfrac{19}{2}=9.5.

III. Solve the equation 2y+14=4y-2:

14+2=4y-2y,\\ \\16=2y,\\ \\y=16:2=8.

f(3)=2*3+2=8

f-1=(3x-4)/5-1=(3x-4-5)/5=(3x-9)/5  => f-1(4)=[(3*4)-9]/5=3/5

y+10=2y+1 => y=9

I. ) f ( 3 ) = 36 + 2 = 8
II. ) f ( x ) = ( 3 x - 4 ) / 5
y = ( 3 x - 4 ) / 5
5 y = 3 x - 4
5 y + 4 = 3 x
x = ( 5 y + 4 ) / 3
f-1(x ) = ( 5 x + 4 ) /3
f-1(4) = ( 20 + 4 ) / 3 = 24/3 = 8
III. ) y + 10 = 2 y + 1
- y = - 9
y = 9
The same result have I. and II.


Do you know the answer?

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