Step-by-step explanation:
( i )
\begin{gathered}p(x) = 4x^2 -3x + 7\\\\p(1) = 4(1)^2 - 3(1) + 7 = 4 - 3 + 7 = 1 + 7 = 8\end{gathered}
p(x)=4x
2
−3x+7
p(1)=4(1)
2
−3(1)+7=4−3+7=1+7=8
( ii)
\begin{gathered}q(y) = 2y ^3 -4y + \sqrt{11}\\\\q(1) = 2( 1)^3 - 4(1) + \sqrt{11} = 2 - 4 + \sqrt{11} = -2 + \sqrt{11}\end{gathered}
q(y)=2y
3
−4y+
11
q(1)=2(1)
3
−4(1)+
11
=2−4+
11
=−2+
11
(iii)
\begin{gathered}r(t) = 4t^4 + 3t^3 -t^2+6\\\\r(p) = 4(p)^4 + 3(p)^3 - (p)^2 + 6= 4p^4 + 3p^3 -p^2 + 6\end{gathered}
r(t)=4t
4
+3t
3
−t
2
+6
r(p)=4(p)
4
+3(p)
3
−(p)
2
+6=4p
4
+3p
3
−p
2
+6
(iv)
\begin{gathered}s(z) = z^3 -1\\s(1) = (1)^3 -1 = 1 - 1 = 0\end{gathered}
s(z)=z
3
−1
s(1)=(1)
3
−1=1−1=0
(v)
\begin{gathered}p(x) = 3x^2+5x-7 \\\\p(1) = 3(1)^2 + 5(1) - 7 = 3 + 5 - 7 = 8 - 7 = 1\end{gathered}
p(x)=3x
2
+5x−7
p(1)=3(1)
2
+5(1)−7=3+5−7=8−7=1
(vi)
\begin{gathered}q(z) =5z^3 -4z +\sqrt{2}\\\\q(2) = 5(2)^3 - 4(2) \sqrt2 = (5 \times 8) - ( 4 \times 2) + \sqrt 2 = 40 - 8 + \sqrt 2 = 32 + \sqrt2\end{gathered}
q(z)=5z
3
−4z+
2
q(2)=5(2)
3
−4(2)
2
=(5×8)−(4×2)+
2
=40−8+
2
=32+
2
