Answered

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- the function g is defined by g(x) = 7-2x²-12x for x>k
- state the smallest value of k for which g
has an inverse,

Sagot :

sqdancefan

Answer:

  -3

Step-by-step explanation:

You want the smallest k such that g(x) = 7-2x²-12x has an inverse function for x>k.

Inverse function

The inverse of g(x) will exist if it passes the horizontal line test. That is, a horizontal line can intersect g(x) in no more than one place.

This will be the case when x-values are restricted to those greater than the x-value of the line of symmetry.

Line of symmetry

The line of symmetry of function g(x) = ax² +bx +c is given by ...

  x = -b/(2a)

The given function has a=-2, b=-12, and c=7. The line of symmetry is ...

  x = -(-12)/(2(-2)) = 12/-4 = -3

g(x) will have an inverse for all x > -3.

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