Find the Domain of the Function F and of Its $\mathrm { f } ^ { - 1 }$

question 255

Multiple Choice

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .
- $$f ( x ) = \tan ( x - 4 ) + 7$$

• A) Domain of f: \(( \infty , \infty )\)
• Domain of \(\mathrm { f } ^ { - 1 } : [ - 8 , - 6 ]\)
• B) Domain of \(f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } + 7 ; k\) an integer
• Domain of \(\mathrm { f } ^ { - 1 } : ( \infty , \infty )\)
• C) Domain of \(f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k\) an integer
• Domain of \(\mathrm { f } ^ { - 1 } : ( \infty , \infty )\)
• D) Domain of \(\mathrm { f } : [ - 4,4 ]\)
• Domain of \(\mathrm { f } ^ { - 1 } : ( \infty , \infty )\)

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Definitions:

Gross Motor Coordination

The ability to use large muscles to perform tasks like walking, jumping, and maintaining balance.

Fine Motor Skills

The coordination of small muscle movements usually involving the synchronization of hands and fingers with the eyes.

Voluntarily Grasp

The intentional action of closing the hand and holding onto something, seen as an important motor skill development in infants.

Developmental Lag

A delay in reaching specific developmental milestones compared to the average timeline for those milestones.