+619 a) Suppose f(x)=95x−4. Does $f$ have an inverse? If so, find $f^{-1}(20)$.
b) Suppose g(x)=4x2+8x+13. Does $g$ have an inverse? If so, find $g^{-1}(25)$
c) Suppose h(x)=1√x for $x>0$. Does $h$ have an inverse? If so, find $h^{-1}(4)$.
+9488 a) f(x) = 95x - 4 This has an inverse because it is just a linear equation.
y = 95x - 4 To find the inverse, solve this equation for x , so add 4 to both sides.
y + 4 = 95x Multiply both sides by 59 .
59(y + 4) = x So the inverse function is...
f-1(x) = 59(x + 4) And to find f-1(20) , plug in 20 for x into this function.
f-1(20) = 59(20 + 4) = 59(24) = 403
b) g(x) = 4x2 + 8x + 13
g(x) does not have an inverse function because it would have two different y values for an x value, and for an equaton to qualify as a function, there can only be one y value for every x value.
c) h(x) = 1√x for x > 0 Yes this has an inverse.
y = 1√x To find the inverse, solve this equation for x .
y√x = 1
√x = 1y Square both sides.
x = 1y2 So the inverse function is..
f-1(x) = 1x2 for x > 0
f-1(4) = 142 = 116
+9488 a) f(x) = 95x - 4 This has an inverse because it is just a linear equation.
y = 95x - 4 To find the inverse, solve this equation for x , so add 4 to both sides.
y + 4 = 95x Multiply both sides by 59 .
59(y + 4) = x So the inverse function is...
f-1(x) = 59(x + 4) And to find f-1(20) , plug in 20 for x into this function.
f-1(20) = 59(20 + 4) = 59(24) = 403
b) g(x) = 4x2 + 8x + 13
g(x) does not have an inverse function because it would have two different y values for an x value, and for an equaton to qualify as a function, there can only be one y value for every x value.
c) h(x) = 1√x for x > 0 Yes this has an inverse.
y = 1√x To find the inverse, solve this equation for x .
y√x = 1
√x = 1y Square both sides.
x = 1y2 So the inverse function is..
f-1(x) = 1x2 for x > 0
f-1(4) = 142 = 116
