Finding the composite function g(f(x)) with linear and radical functions

Aprilshowers · Jul 13, 2005

If f(x) = 3x + 1
and g(x) = (x^2 + 5x)^-1/2
find g(f(x))

Aprilshowers · Jul 13, 2005

Does this look right?

f(x) = 3x + 1
g(b) = (b^2 + 5b)^-1/2
Let b=f(x)=3x+1
Substitute 3x + 1 in for b:
g(b)=((3x+1)^2+5* (3x+1))^-.5
=(9x^2+6x+1+15x+5)^-.5
=(9x^2+21x+6)^-.5
g(f(x))= (9x^2+21x+6)^-.5
Please advise

HallsofIvy · Jul 13, 2005

Yes, that's exactly right. To find g(f(x)) you replace the "x" in the formula for g with the formula for f(x).

Finding the composite function g(f(x)) with linear and radical functions

Discussion

Why does adiabatic compression use more energy than adiabatic expansion?

What force causes precession?

Simple kinematics problem — falling from a geostationary satellite

Why does a fan cool you in a sealed room if it adds heat?

If Heat Is Motion, Why Isn’t All Motion Heat?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Finding the composite function g(f(x)) with linear and radical functions

Discussion

Similar threads

High School Deriving v(t) from F(x), for Linear Motion

Undergrad Limit Calculation for Radical Functions

High School Finding points with horizontal tangent lines for rational and radical functions