Functions (general)

For the inverse trigonometric functions, what must be true about their original functions?

• They must be one-to-one on their restricted domains.

• They must be periodic on all domains.

• They must have a range of all real numbers.

• They must intersect the line y = x.

Which statement is true for the graph of the inverse tangent function?

• It has a range of all real numbers.

• It has a domain of [-π, π].

• It is not a one-to-one function.

• It passes the horizontal line test.

What is the range of the inverse tangent function?

• [-1, 1]

• [0, π]

• [-π/2, π/2]

• (-π/2, π/2)

What is the inverse of

 $h\left(x\right)=x^2+1,\ x\ge0$  ?

•  $h^{-1}\left(x\right)=\sqrt{x-1}$  

• B.  $f^{-1}\left(x\right)=\sqrt{x-1}$  

• C.  $h^{-1}\left(x\right)=-\sqrt{x-1}$  

• D.  both A and B

Mathematical Equivalence

ON

Which of the following Domain Restriction would keep the inverse NOT A FUNCTION?

Which inverse trigonometric function is this?

• arctan

• arcctn

• arcsec

• arccsc

What is the inverse of sqrt(x-4)+1?

• (x-1)²+4
• (x-1)²+4 domain restricted to x>= 1
• (x+1)²+4  domain restricted to x>= 0
•  (x+1)²+4 domain restricted to x>= -1

• Minor (-)

• Add (+)

Find the inverse of the function including any restriction on domain

• f^-1 = (x² + 2),  x ≤ 0
• f^-1 = (x² + 1) / 2,  x ≤ 0
• f^-1 = (x² − 1) / 2,  x ≥ 0
• Inverse does not exist