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g(m)=m^(3) h(m)=(m^(2))/(m+3) Evaluate. (g@h)(6)=

g(m)=m3 g(m)=m^{3} \newlineh(m)=m2m+3 h(m)=\frac{m^{2}}{m+3} \newlineEvaluate.\newline(g∘h)(6)= (g \circ h)(6)=

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Q. g(m)=m3 g(m)=m^{3} \newlineh(m)=m2m+3 h(m)=\frac{m^{2}}{m+3} \newlineEvaluate.\newline(g∘h)(6)= (g \circ h)(6)=
  1. Understand Function Composition: Understand the composition of functions. The composition of two functions g(m)g(m) and h(m)h(m), denoted as (g@h)(m)(g@h)(m), means that we first apply h(m)h(m) and then apply gg to the result of h(m)h(m).
  2. Evaluate h(m)h(m) at m=6m=6: Evaluate h(m)h(m) at m=6m=6.
    h(m)=m2m+3h(m) = \frac{m^2}{m + 3}
    h(6)=626+3h(6) = \frac{6^2}{6 + 3}
    h(6)=369h(6) = \frac{36}{9}
    h(6)=4h(6) = 4
  3. Evaluate g(m)g(m) at Result: Evaluate g(m)g(m) at the result from Step 22.\newlineSince h(6)=4h(6) = 4, we now evaluate g(m)g(m) at m=4m=4.\newlineg(m)=m3g(m) = m^3\newlineg(4)=43g(4) = 4^3\newlineg(4)=64g(4) = 64
  4. Conclude Composition Value: Conclude the value of the composition (g@h)(6)(g@h)(6). Since g(h(6))=g(4)g(h(6)) = g(4), we have: (g@h)(6)=64(g@h)(6) = 64

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