Answer:
(1)
[tex]f(x)=3(\frac{1}{3})^x[/tex]
[tex]g(x)=3(\frac{3}{4})^x[/tex]
(2)
[tex](8x-9-2x)(15+5x-5)=30x^2+15x-90[/tex]
(3)
[tex](x-8)^2=52[/tex]
Step-by-step explanation:
(1)
Calculation of f(x):
we can use exponential function formula
[tex]f(x)=a(b)^x[/tex]
we can select any two points to find 'a' and 'b
At x=0 , y=3:
we can plug values
[tex]f(0)=a(b)^0[/tex]
[tex]3=a(b)^0[/tex]
[tex]a=3[/tex]
now, we can plug it back
[tex]f(x)=3(b)^x[/tex]
At x=-1 , y=9:
[tex]f(-1)=3(b)^{-1}[/tex]
[tex]9=3(b)^{-1}[/tex]
[tex]b=\frac{1}{3}[/tex]
now, we can plug it back
[tex]f(x)=3(\frac{1}{3})^x[/tex]
Calculation of g(x):
we can use exponential function formula
[tex]g(x)=a(b)^x[/tex]
we can select any two points to find 'a' and 'b
At x=0 , y=3:
we can plug values
[tex]f(0)=a(b)^0[/tex]
[tex]3=a(b)^0[/tex]
[tex]a=3[/tex]
now, we can plug it back
[tex]g(x)=3(b)^x[/tex]
At x=1 , y=4:
[tex]g(1)=3(b)^{1}[/tex]
[tex]4=3(b)^{-1}[/tex]
[tex]b=\frac{3}{4}[/tex]
now, we can plug it back
[tex]g(x)=3(\frac{3}{4})^x[/tex]
(2)
we are given
[tex](8x-9-2x)(15+5x-5)[/tex]
we can combine like terms
[tex](8x-2x-9)(5x+15-5)[/tex]
[tex](6x-9)(5x+10)[/tex]
we can distribute it
[tex]=6x\cdot \:5x+6x\cdot \:10+\left(-9\right)\cdot \:5x+\left(-9\right)\cdot \:10[/tex]
[tex]=6\cdot \:5xx+6\cdot \:10x-9\cdot \:5x-9\cdot \:10[/tex]
[tex]=30x^2+15x-90[/tex]
(3)
we are given
[tex]x^2-16x+12=0[/tex]
Subtract both sides by 12
[tex]x^2-16x+12-12=0-12[/tex]
[tex]x^2-16x=-12[/tex]
We can complete square
[tex]x^2-2\times 8\times x=-12[/tex]
we can add 8^2 both sides
[tex]x^2-2\times 8\times x+8^2=-12+8^2[/tex]
[tex](x-8)^2=-12+8^2[/tex]
[tex](x-8)^2=-12+64[/tex]
[tex](x-8)^2=52[/tex]
