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# Common Core Standard HSF-BF.B.4a Questions

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.

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Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse. $f(x) = 1/5 x^3$
1. $f^{-1}(x) = 5root[3](x)$
2. $f^{-1}(x) = root[3](5x)$
3. $f^{-1}(x) = root[3](1/5 x)$
4. $f^{-1}(x) = 1/5root[3](x)$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse. $f(x) = (x-8)/(x+1)$
1. $f^{-1}(x) = (x-1)/(x+8)$
2. $f^{-1}(x) = -9/(x+1)$
3. $f^{-1}(x) = (-x-8)/(x-1)$
4. $f^{-1}(x) = (x-8)/x$
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of $f(x) = 1/2 x + 4/5$.
1. $f^{-1}(x) = 2x - 8/5$
2. $f^{-1}(x) = 2x - 4/5$
3. $f^{-1}(x) = -1/2 x - 4/5$
4. $f^{-1}(x) = -2x - 5/4$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. $f(x) = e^(x^3)$
1. This function has no inverse.
2. $f^{-1}(x) = ln(x^3)$
3. $f^{-1}(x) = ln(root[3](x))$
4. $f^{-1}(x) = root[3](ln(x))$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of $g(x)=-3x$.
1. $g ^(-1) (x)=x+1$
2. $g ^-1 (x)=-3x-3$
3. $g ^-1 (x)=x-1$
4. $g ^-1(x)= -1/3 x$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the function $g(x) = -4x + 1$.
1. $g^(-1)(x) = 1 /(x+3)$
2. $g^(-1)(x) = 3 /(x+2)$
3. $g^(-1)(x) = 1 /(x+2)$
4. $g^(-1)(x) = (-x+1) /4$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which is the inverse of $f(x)=2x-7$?
1. $f^-1(x)=2/7(x+1)$
2. $f^-1(x)=2/7x+7$
3. $f^-1(x)=(x+7)/2$
4. $f^-1(x)=x/2+7$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse for the function.
$f(x)=-3/4x+5$
1. $f^-1(x)=(3x-5)/4$
2. $f^-1(x)=3/4(x-5)$
3. $f^-1(x)=(-4x-5)/3$
4. $f^-1(x)=(-4x+20)/3$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Match each function with its inverse.
 __ $f(x) = 3 ln(x+2)$ A. $f^{-1} (x) = e^(x//3) -2$ __ $f(x) = e^(5x+2)$ B. $f^{-1} (x) = (ln(x)-2)/5$ __ $f(x) = log(3x)/2$ C. $f^{-1} (x) = log(x-5) + 2$ __ $f(x) = 10^{x-2} + 5$ D. $f^{-1} (x) = 10^{2x}/3$
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the function $f(x) = 3x-2$.
1. $f^{-1}(x) = 1/3 x + 2$
2. $f^{-1}(x) = x +2$
3. $f^{-1}(x) = x + 2/3$
4. $f^{-1}(x) = 1/3 x + 2/3$
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of $f(x) = x$.
1. $f^{-1}(x) = x$
2. $f^{-1}(x) = y$
3. $f^{-1}(x) = 1$
4. $f^{-1}(x) = 1/x$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. $f(x) = 4x^3 + 2$
1. $f^{-1}(x) = (x^3-2)/4$
2. $f^{-1}(x) = (root[3](x) - 2)/4$
3. $f^{-1}(x) = root[3]((x-2)/4)$
4. $f^{-1}(x) = root[3](x-2)/4$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
What is the inverse of $f(x) = 3/(x-1) ?$
1. $f^{-1}(x) = (x+1)/3$
2. $f^{-1}(x) = (x+3)/x$
3. $f^{-1}(x) = 3/(x+1)$
4. $f^{-1}(x) = 4/x$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. $f(x) = 3^{9x-5}$
1. $f^{-1}(x) = log_3(1/9 x + 5)$
2. $f^{-1}(x) = log_3(x/9) + 5$
3. $f^{-1}(x) = log_3(x+5)/9$
4. $f^{-1}(x) = (log_3(x) + 5)/9$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
If $f(x) = log_4(3x-1) + 10$, what is the inverse of this function?
1. $f^{-1}(x) = (4^(x-10)+1)/3$
2. $f^{-1}(x) = 4(x/3 + 1) - 10$
3. $f^{-1}(x) = 1/3 (4^x -9)$
4. $f^{-1}(x) = 4^((x-10)/3 + 1)$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which of the following functions is the inverse of $y=3x+5$?
1. $-y=-3x-5$
2. $y=(x-5)/3$
3. $x=3y+5$
4. $y=1/3x-5$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which of the following is the inverse of $y=(5x^2+4)/3, x>=0$?
1. $-y=+-sqrt(5x^2)+3/4$
2. $-y=(-5x^2-4)/-3$
3. $x=(5y^2+4)/3$
4. $y=sqrt((3x-4)/5)$
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which of the following is the inverse of $y=x^2+4, x<=0$ ?
1. $-y=sqrt(x-4)$
2. $y=+-sqrt(x)-2$
3. $x=+-sqrt(y^2+4)$
4. $y=sqrt(x)-4$
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