Question

function operations
given the function $f(x) = 2x - 4$ and the function $g(x) = 6x^2 + 5x + 14$ determine each of the following.
give your answer as a whole number or a simplified fraction.
evaluate $10f(3) + g(7)$
$10f(3) + g(7) = $
evaluate $g(4) - 12f(5)$
$g(4) - 12f(5) = $
evaluate $f(8) \cdot g(12)$
$f(8) \cdot g(12) = $
evaluate $\frac{g(2)}{5f(10)}$
$\frac{g(2)}{5f(10)} = $
question help: video

Explanation:

Step1: Calculate $f(3)$

$f(3)=2(3)-4=6-4=2$

Step2: Calculate $g(7)$

$g(7)=6(7)^2+5(7)+14=6(49)+35+14=294+35+14=343$

Step3: Compute $10f(3)+g(7)$

$10(2)+343=20+343=363$

Step4: Calculate $g(4)$

$g(4)=6(4)^2+5(4)+14=6(16)+20+14=96+20+14=130$

Step5: Calculate $f(5)$

$f(5)=2(5)-4=10-4=6$

Step6: Compute $g(4)-12f(5)$

$130-12(6)=130-72=58$

Step7: Calculate $f(8)$

$f(8)=2(8)-4=16-4=12$

Step8: Calculate $g(12)$

$g(12)=6(12)^2+5(12)+14=6(144)+60+14=864+60+14=938$

Step9: Compute $f(8)\cdot g(12)$

$12\times938=11256$

Step10: Calculate $g(2)$

$g(2)=6(2)^2+5(2)+14=6(4)+10+14=24+10+14=48$

Step11: Calculate $f(10)$

$f(10)=2(10)-4=20-4=16$

Step12: Compute $\frac{g(2)}{5f(10)}$

$\frac{48}{5(16)}=\frac{48}{80}=\frac{3}{5}$

Answer:

$10f(3)+g(7)=363$
$g(4)-12f(5)=58$
$f(8)\cdot g(12)=11256$
$\frac{g(2)}{5f(10)}=\frac{3}{5}$