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The curve \(f(x)=x^2\) is transformed to \(g(x)=3 f[2(x+2)]\)
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a. \(g(x)=12(x+2)^2\)
b. \(\left( -\dfrac{7}{2}, 27 \right) \)
| a. | \(g(x)\) | \(=3[2(x+2)]^2\) |
| \(=3 \times 4(x+2)^2\) | ||
| \(=12(x+2)^2\) |
b. \(P(-3,9)\ \text{lies on}\ \ f(x)=x^2 \)
\(\text{Find corresponding point on}\ f(x)\)
\(\text{Mapping}\ x_f\ \text{to}\ x_g: \)
\(2(x_g +2)=x_f\ \ \Rightarrow\ \ x_g=\dfrac{1}{2} x_f-2 \)
\(x_g=\dfrac {1}{2} \times -3 -2=-\dfrac{7}{2} \)
\(\text{Mapping}\ y_f\ \text{to}\ y_g: \)
\(y_g=3 \times y_f = 3 \times 9=27\)
\(\therefore\ \text{Corresponding point}\ = \left( -\dfrac{7}{2}, 27 \right) \)