SOLUTION: Determine the equation for h(x), where {{{ h(x) = k*(g-f) }}} {{{ f(x)= sqrt (x)-2 }}} {{{ g(x)= 2(x^2+1)-1 }}} {{{ k(x)= x+4 }}} a. {{{ h(x)= -2x^2+x+9 }}} b. {{{ h(x)= -

Algebra ->  Functions -> SOLUTION: Determine the equation for h(x), where {{{ h(x) = k*(g-f) }}} {{{ f(x)= sqrt (x)-2 }}} {{{ g(x)= 2(x^2+1)-1 }}} {{{ k(x)= x+4 }}} a. {{{ h(x)= -2x^2+x+9 }}} b. {{{ h(x)= -      Log On


   

Question 952437: Determine the equation for h(x), where +h%28x%29+=+k%2A%28g-f%29+
+f%28x%29=+sqrt+%28x%29-2+
+g%28x%29=+2%28x%5E2%2B1%29-1+
+k%28x%29=+x%2B4+
a. +h%28x%29=+-2x%5E2%2Bx%2B9+
b. +h%28x%29=+-2x%5E2%2Bsqrt+%28x%29%2B7+
c. +h%28x%29=+2x%5E2-sqrt+%28x%29%2B7+
d. +h%28x%29=+2x%5E2-x%2B7+
Thank you.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation for h(x), where +h%28x%29+=+k%2A%28g-f%29+
+f%28x%29=+sqrt+%28x%29-2+
+g%28x%29=+2%28x%5E2%2B1%29-1+
+k%28x%29=+x%2B4+

if you have +h%28x%29+=+k%2A%28g-f%29+, then
+h%28x%29+=+%28x%2B4%29%2A%28%282%28x%5E2%2B1%29-1%29-%28sqrt+%28x%29-2%29%29+
+h%28x%29+=+%28x%2B4%29%2A%282x%5E2%2B2-1-sqrt%28x%29%2B2%29+
+h%28x%29+=+%28x%2B4%29%2A%282x%5E2%2B1-sqrt%28x%29%2B2%29+
+h%28x%29+=+%28x%2B4%29%2A%282x%5E2-sqrt%28x%29%2B3%29+ if you multiply further, you will have function of degree 3

+h%28x%29+=2x%5E3%2B8x%5E2%2B3x-x%2Asqrt%28x%29-4sqrt%28x%29%2B12+
+h%28x%29+=2x%5E3%2B8x%5E2%2B%283-sqrt%28x%29%29x-4sqrt%28x%29%2B12+
since your answer options are these:
a. +h%28x%29=+-2x%5E2%2Bx%2B9+
b. +h%28x%29=+-2x%5E2%2Bsqrt+%28x%29%2B7+
c. +h%28x%29=+2x%5E2-sqrt+%28x%29%2B7+
d. +h%28x%29=+2x%5E2-x%2B7+
we can see that none of them is right answer; so, +h%28x%29+=2x%5E3%2B8x%5E2%2B%283-sqrt%28x%29%29x-4sqrt%28x%29%2B12+ should be your answer