Question 1182273
If f(x) = 1/4x+2 and  g(x) = −3x^2+2, determine the value of -3 g(1) and f^-1 (1).
<pre>Let's separate the stating of the two problems:</pre>
If f(x) = (1/4)x+2, determine the value of f<sup>-1</sup>(1).<pre>
We find f<sup>-1</sup>(x)

a. Replace f(x) by y

{{{y=expr(1/4)*x+2}}}

b. Interchange x and y.

{{{x=expr(1/4)*y+2}}}

c. solve for y

Multiply through by 4 to clear the fraction:

{{{4x = y+8}}}

{{{4x-8=y}}}

{{{y=4x-8}}}

d. replace y by f<sup>-1</sup>(x)

f<sup>-1</sup>(x) = 4x-8

Therefore,

f<sup>-1</sup>(1) = 4(1)-8
f<sup>-1</sup>(1) = 4-8
f<sup>-1</sup>(1) = -4

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</pre>If g(x) = −3x<sup>2</sup>+2, determine the value of -3g(1).<pre>

   g(1) = −3(1)<sup>2</sup>+2
   g(1) = −3(1)+2
   g(1) = -3+2
   g(1) = -1

Therefore multiply both sides by -3:
 
 -3g(1) = -3(-1)
 -2g(1) = 3

Edwin</pre>