Radical Functions

Question

Given f(x)=4√x+5f(x)=4x+5, solve f(x)=12f(x)=12

x=

Given f(r)=√r+44−rf(r)=r+44-r, solve f(r)=2f(r)=2

r=

Answer 1

1) f(x)=4√x +5f(x)=4x+5 so we have two equations f(x)=4x+5 and f(x)=4√x +5f(x) ⇔4x+5=4√x +5f(x) ⇔

5f(x)=4x-4√x+5 ⇔f(x)=(4/5)x-(4/5)√x+1 we have to solve the equation 12f(x)=12 ⇔ f(x)=1⇔

(4/5)x-(4/5)√x+1=1⇔(4/5)x-(4/5)√x=0 ⇔4/5(x-√x)=0⇔x-√x=0⇔x=√x⇔x=1

2) Given f(r)=√r+44−rf(r)=r+44-r, solve f(r)=2f(r)=2

f(r)=44 and f(r)=√r+44−rf(r) ⇔ 44=√r+44−rf(r) ⇔√r−rf(r)=0⇔f(r)=√r/r

⇔

solve f(r)=2f(r)=2 ⇔ f(r)=1 ⇔√r/r=1⇔√r/r -1=0⇔(√r-r)/r=0⇔(√r-r)=0⇔(√r=r) ⇔r=1