4. Suppose you make $12 an hour as a lifeguard at the community pool during the summer. Let h
1 answer:
You might be interested in
Problem 1)
(-3,9) is one point on the original function, so (9,-3) is on the inverse. We swap x and y. The point (9,-3) isn't listed so we move onto the next.
(-1,1) is on the original so (1,-1) is on the inverse. Again we swap x and y. Choice D matches with this. So D is one of the answers.
Choice A is also an answer since (0,0) swaps to (0,0)
Choice C is also an answer since (2,4) swaps to (4,2)
In summary, the answers are A, C, D
======================================================================
Problem 2)
Replace f(x) with y. Swap x and y. Then solve for y
f(x) = 4x+3
y = 4x+3
x = 4y+3
x-3 = 4y+3-3
x-3 = 4y
4y = x-3
4y/4 = (x-3)/4
y = (x-3)/4
y = x/4-3/4
y = (1/4)x-3/4
which matches with choice A, so choice A is the answer
======================================================================
Problem 3)
Replace g(x) with y. Swap x and y. Then solve for y
g(x) = (-4/3)x + 2
y = (-4/3)x + 2
x = (-4/3)y + 2
x-2 = (-4/3)y + 2-2
x-2 = (-4/3)y
(-3/4)(x-2) = (-3/4)(-4/3)y
(-3/4)(x-2) = y
y = (-3/4)(x-2)
y = (-3/4)x+(-3/4)(-2)
y = (-3/4)x+3/2 ... answer is choice C
======================================================================
Problem 4)
The first two are invertible while the last two are not. The last two fail the horizontal line test so they don't have an inverse.
======================================================================
Problem 5)
It's a bit tricky to determine what the answer choices are saying but I'm assuming they are referring to fourth roots. If so, then we have
f(x) = x^4+7
y = x^4+7
x = y^4+7
x-7 = y^4+7-7
x-7 = y^4
y^4 = x-7
FourthRoot(y^4) = FourthRoot(x-7)
y = FourthRoot(x-7)
which is written as![\sqrt[4]{x-7}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx-7%7D)
(-3,9) is one point on the original function, so (9,-3) is on the inverse. We swap x and y. The point (9,-3) isn't listed so we move onto the next.
(-1,1) is on the original so (1,-1) is on the inverse. Again we swap x and y. Choice D matches with this. So D is one of the answers.
Choice A is also an answer since (0,0) swaps to (0,0)
Choice C is also an answer since (2,4) swaps to (4,2)
In summary, the answers are A, C, D
======================================================================
Problem 2)
Replace f(x) with y. Swap x and y. Then solve for y
f(x) = 4x+3
y = 4x+3
x = 4y+3
x-3 = 4y+3-3
x-3 = 4y
4y = x-3
4y/4 = (x-3)/4
y = (x-3)/4
y = x/4-3/4
y = (1/4)x-3/4
which matches with choice A, so choice A is the answer
======================================================================
Problem 3)
Replace g(x) with y. Swap x and y. Then solve for y
g(x) = (-4/3)x + 2
y = (-4/3)x + 2
x = (-4/3)y + 2
x-2 = (-4/3)y + 2-2
x-2 = (-4/3)y
(-3/4)(x-2) = (-3/4)(-4/3)y
(-3/4)(x-2) = y
y = (-3/4)(x-2)
y = (-3/4)x+(-3/4)(-2)
y = (-3/4)x+3/2 ... answer is choice C
======================================================================
Problem 4)
The first two are invertible while the last two are not. The last two fail the horizontal line test so they don't have an inverse.
======================================================================
Problem 5)
It's a bit tricky to determine what the answer choices are saying but I'm assuming they are referring to fourth roots. If so, then we have
f(x) = x^4+7
y = x^4+7
x = y^4+7
x-7 = y^4+7-7
x-7 = y^4
y^4 = x-7
FourthRoot(y^4) = FourthRoot(x-7)
y = FourthRoot(x-7)
which is written as