Given the function g(x) = 1/2x^2 + 5x - 1 evaluate each of the following :

Question

Given the function g(x) = 1/2x^2 + 5x - 1 evaluate each of the following :

 

(a) g (-4)

(b) g(d)

(c) g(x^4)

(d) g(4x - 5)

 

(a) g(-4)= ?

Answer 1

Hi Keith;

g(x) = 1/2x^2 + 5x - 1

I think this is...

g(x)=(1/2)x²+5x-1......Please let me know if I am mistaken.

 

(a) g (-4)

g(-4)=[(1/2)(-4)²]+[(5)(-4)]-1

y=[(1/2)(16)]+(-20)_1

y=8-21+1

y=12

 

(b) g(d)

g(x)=(1/2)d²+5d-1

(c) g(x^4)

g(x⁴)={(1/2)[(x⁴)²]}+5x⁴-1

(x⁴)²....the exponentials must be multiplied together, (4)(2)=8

g(x⁴)=[(1/2)x⁸]+5x⁴-1

(d) g(4x - 5)

g(4x-5)={(1/2)[(4x-5)²]}+[5(4x-5)]-1

(4x-5)²=(4x-5)(4x-5)

This must be FOILed...

FIRST...(4x)(4x)=16x²

OUTER...(4x)(-5)=-20x

INNER...(-5)(4x)=-20x

LAST...(-5)(-5)=25

16x²-20x-20x+25

16x²-40x+25

g(4x-5)=[(1/2)(16x²-40x+25)]+[5(4x-5)]-1

g(4x-5)=8x²-20x+12.5+20x-25-1

g(4x-5)=8x²-13.5